Why is the candela a base unit of the SI? The candela is defined as 

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540\cdot10^{12}$ hertz and that has a radiant intensity in that direction of $1/683$ watt per steradian.

Now, I don't see any reason why luminous intensity should be a base unit. I mean, we can just as simply specify the luminous intensity of any source in terms of its frequency and radiant intensity. It seems (to me) that luminous intensity has just been used to clump the two parameters together.  
Contrast this with the definition of a meter

The meter is the length of the path travelled by light in vacuum during a time interval of $1/299 792 458$ of a second.

Now, in the definition of a meter there is one key player, namely light. Even though this definition is given in terms of second (as candela is given in terms of frequency and radiant intensity) but it also refers to a fixed fundamental 'thing' in nature: light. It is primarily on the properties of light that this definition is based, and we require experimentation to determine the 'length' of a meter. This is similar to the definition for a second which refers to an actual real-world object, namely a cesium atom. 
But I see no such reference in the definition of a candela. Why is candela a base SI unit then?
EDIT: As pointed out by some in the comments below, apparently candela has been chosen as a base unit considering its usefulness in other fields (quite unrelated to physics). So I guess my question is modified then to: Is there any rationale from the standpoint of physics to choose candela as a base SI unit?
 A: 
Is there any rationale from the standpoint of physics to choose candela as a base SI unit?

That's still the wrong question. The right question: Why do these standards (any of them) exist? The answer is commerce and industry. The SI doesn't exist to support the sciences; that it does support the sciences is a nice side benefit. It exists to support humans, and in particular, commerce and industry.
We humans rely extensively on vision. It is arguably our most important sense. We need artificial lighting to make our modern world possible. Standards for lighting are important. People make mistakes in low lighting, get headaches in overly bright lighting. The use of 540 terahertz in the definition of the candela is anything but arbitrary. That is where the human vision system peaks. The factor of 1/683 -- that's to make the physics-based definition of the candela consistent with older definitions. Consistency is very important in metrology. Consistency is the reason for that seemingly arbitrary factor of 1/299792458 used in the definition of the meter.

As an aside, there are lots of physicists who don't use SI units. To an astrophysicist, the second, meter, and kilogram are too small. They tend to use years (qualified with kilo, mega, giga) for time, astronomical units or parsecs for distance, and the mass of the Sun as their base units. To a particle physicist, the second, meter, and kilogram are too big, and also are not particularly meaningful. Particle physicists view energy as a base concept (as opposed to mass, which is just one of many forms of energy). To a theoretical physicist, the SI is but a tiny step toward a consistent set of units. As far as a theoretical physicist is concerned, SI is little better than the customary units still used in the US. 
A: That definition is for calibration. Luminosity is based on a standardized model of human eye and takes into account sensitivity of human eye to different wavelengths. Two source with the same intensity but different frequency have different luminosity. Luminosity is related to intensity and frequency by the luminosity function.
A: The point is that luminous intensity is intensity as perceived by the human eye, and particularly taking into account the fact that the same amount of power will be perceived as brighter or dimmer depending on whether the wavelength is at a maximum of the eye's sensibility or at a minimum. 
This makes the candela ever so slightly washier than the other six SI base units, because you need to rely on physiological measurements of the average human, whoever that is, but the simple fact is that you cannot measure how bright a light looks to a human eye using just stopwatches, yardsticks and weights - you need to use the eye itself as a measurement device, or at the very least calibrate with one. Luminous intensity is a measure of the biological response of a specific system (if not of the subjective perception this response causes), and unless you're willing to define the unit of luminous intensity in terms of neuron activity on the optical nerve then you really do need a unit of measurement that's independent of the mks triplet.
In general, suppose your eye receives light from a source with a radiant intensity of 
$$I_\mathrm{r.i.}=(I_\mathrm{r.i.})\:\mathrm{W\:sr^{-1}m^{-2}},$$
i.e. each unit area $A$, channelling a pencil of radiation of solid angle $\Omega$ receives $I_\mathrm{r.i.}A\Omega$ joules of radiated energy per second. This still doesn't tell you how bright the source will look to you, though, because the different receptors are more or less sensitive to radiation at different wavelengths. However, this dependence has been quite thoroughly studied using a number of methods, which have resulted in a fairly standard luminosity function: that is, a function 
$$\bar{y}(\lambda),\text{ also denoted }V(\lambda),$$
that tells you how bright lights look at different wavelengths. Thus if $\bar{y}(\lambda_1)/\bar{y}(\lambda_2)=2$ then a light at $\lambda_1$ will look twice as bright as a lamp of the same radiant intensity at $\lambda_2$. 
There is of course some individual variation, as well as the tough metrological problem of measuring and standardizing the luminosity function, and controlling for the fact that different populations can have different average responses, but that's all in the game and it's ultimately someone else's (i.e. not a physicist's) business. And if you want to really go down the rabbit hole, you need to control for the fact that the perceived intensity will vary under well-lit versus low-light conditions, and down and down it goes. However, you only need to normalize once for each set of conditions; hence the value of standard candles.
The candela comes in, essentially, as the units of the standard luminosity function. A light source of wavelength $\lambda$ and radiant intensity $I_\mathrm{r.i.}$ will have a (perceived) luminous intensity
$$I_\mathrm{l.i.}=\bar{y}(\lambda)I_\mathrm{r.i.},$$
where now the luminous intensity $I_\mathrm{l.i.}$ is a completely different beast to the radiant intensity, depending as it does on a human reaction, so it is measured in candela. It follows, then, that the luminosity function has units of $\mathrm{cd}/(\mathrm{W\:sr^{-1}m^{-2}})$, and the role of the SI definition is to normalize it such that
$$\bar{y}(555\:\mathrm{nm})=\frac{1\:\mathrm{cd}}{\mathrm{W\:sr^{-1}m^{-2}}}.$$
From here one can then fill out the rest of the curve for $\bar{y}(\lambda)$ using only comparative measurements of (perceived) luminous intensity, which are much easier.
When measuring the "brightness" of a light source, there is a huge number of different quantities of interest, each with their own unit but a very similar name to the others, and depending on exact details like whether you're integrating over angle, or surface, or wavelength, or any combination thereof. It is very easy, as a physicist, to simply give up and reckon that "luminous intensity" will simply be one of the list. Similarly, it's easy to simply slide over terms like photometry and not realize that it's very different to radiometry.
That just means, though, that we need to up our game a bit and realize that there's an extra dimension at play here - the subjective sensation of brightness as perceived by the human eye as a measuring device - that we need to include on an equal footing to our clocks, meter sticks and (soon to be) watt balances, if we really want to produce measurements which are useful in a world inhabited by humans.
A: Personally, from a pure physics point of view, i don't think we need the candela as a base S.I. unit. it seems that all we need is:
m,kg,s,A,K,mol
These can all be related to basic physics constants (see Physics Today, July 2014, p. 37):
c,h,delta nu(pick any atomic transition),e,k(Boltzmann),N_A(Avogadro's)
Actually, even N_A is only necessary from a practical sense of macroscopic measurements. Once that is given up, and N_A is added, then one also includes units like the candela related to human visual perception. Regarding sound perception, to be consistent there should be another unit added such as the loudness level "phon" or loudness scale "sone". We see, we hear, to be consistent, perhaps a human sound scale unit should be included too; it's not never-ending, eight "fundamental" S.I. units seem to sum it up from our current best point of view.
