Why are thermodynamic processes slow? 
Back when I sat through my thermodynamic classes, I remember my physics professor attempting a joke during one of his lecture demonstrations. While waiting for some beaker of water to boil, he warned us of taking a job where we would have to work with thermodynamic phenomena, since "thermodynamics is slow". The joke was that thermodynamics as it is taught in textbooks is equilibrium thermodynamics, concerned with infinitesimal changes, and thus by definition considers only slow changes. But he turned this around and commented on the speed of any thermodynamic process, specifically, waiting for the beaker to boil.

The statement that thermodynamic processes are slow certainly applies to heating pots of water, as evidenced by the proverbial "a watched kettle never boils". Yet it does feel like there is a more fundamental principle at work? Once thermodynamics gets involved in our experiments, the pace slows down considerably. Wait for your dilution fridge to reach base temperature. Wait for temperature to equilibriate across your entire specimen. Compare the speed of sound to essentially any other speed, whether current down a cable or of course that of light. Convection takes ages to have notable effects.
Is this just due to speeds of sound having the relatively slow values they have compared to other speeds found in physics or is there a more fundamental principle at work? (maximum possible information transfer anyone?)
To avoid confusion, I am not asking why (equilibrium) thermodynamics only deals with slow (quasi-static) processes - that is merely by definition of equilibrium thermodynamics. I am asking whether there is a principle or other good reason why thermodynamic processes happen on timescales many orders of magnitude slower than those encountered e.g. in electrodynamics, particle physics, etc.
 A: I think you would get better appreciation of your question on Chemistry SE because chemists usually have a lot of first hand experience with slow thermodynamic processes (although there are also many reactions that are fast, of course).
As far as I understand you, the processes you mean are all somehow related to diffusion/heat conduction. Why is diffusion slower than just pumping a fluid through a pipe? Diffusion processes are characterized by the average directed particle velocity being close to zero, while the standard deviation of velocity (or the average magnitude of velocity) can be quite big. For a fluid flow in a pipe the velocity magnitude is also rather big, but the directed velocity is big too, because the particles move synchronously.
Therefore when a certain particle type needs to move from A to B (in order to react with another component) by diffusion, it actually does that with high speed, but it wastes a lot of time just randomly zigzagging back and forth without being displaced much after all, and, moreover, it has to rely on chance to get significantly displaced (if average directional velocity is zero). So it has a clear disadvantage compared to a bunch of particles of the same type and velocity magnitude, which are moving directionally in a pipe.
So your question basically amounts to asking why it takes a long time to get to the restroom on a very crowded rock concert, while you can get quickly to the toilet in a railway station at midnight, even though the linear distance to the loo might be almost equal in both cases.
Since heat conduction is nothing but a special form of diffusion where energy is transported instead of particle type, the above description applies accordingly.
A: Slow or fast, it is a matter of the relevant time scale used for comparison. It is not the human time scale that should be used, but the microscopic time scale associated with every thermodynamic system's dynamics.
On the human time scale, waiting for water boiling may seem slow, while the freezing of a bottle of supercooled water, or an explosion, may look instantaneous. All these processes are slow compared with the typical microscopic relaxation times (tents or hundredths of picoseconds). However, as noticed in a comment by @JonCuster, pulsed laser melting of silicon surface may require a few picoseconds.
The key point to understand the general slow timescale of thermodynamic processes and understand why some processes may become fast, is the spatial scale.
Thermodynamic systems are usually large macroscopic systems. Moreover, many thermodynamic properties (energy is the first, of course) are local conserved quantities, i.e., their local variation in a volume can only be due to a transport process across the boundary. This, in turn, implies that the larger is the volume, the longer is the relaxation time for any process controlled by conserved quantities. That is also the reason for the importance of the diffusive processes mentioned in @oliver's answer.
Therefore, the slowness of thermodynamic processes is generally due to the size through such a mechanism. This also explains why in some cases, times get faster, like in  laser surface melting. In that case, the size of the thermodynamic system involved by the process is relatively small (far from a mole of atoms).
