Physical quantities are often defined in textbooks as measurable quantities. I find this definition confusing. For example, if you think about it, the number of clothes in a cupboard is also a measurable quantity but it is not a known physical quantity in physics. Please give a definition of physical quantities that withstands scrutiny.
Your "number of clothes" is certainly a physical quantity, for precisely the reason given by your wikipedia cite -- it's measurable by an experimental apparatus. In this case, an apparatus designed for that purpose would be kind of senseless, whereby "universal laws" involving the behavior of such an apparatus would be hard to formulate.
Perhaps your "withstands scrutiny" requirement could then be interpreted precisely in this "formulate laws" sense. Physics concerns itself with those "physical quantities" among which experimental measurements can be mathematically related. The simpler (or "better" in some sense) the relationships, the more fundamental the quantities. So "number of clothes" wouldn't be fundamental whatsoever; however, one way or another, it's certainly physical.
Nobody can really make a measurement without understanding what it is that they're measuring. Is length a physical quantity? How would I measure length? I would put a ruler next to the object in question and see how many tick marks long it is. So I measured the length, right? Well, how do I know which tick mark the object reaches? Light scattered off of the object and the ruler, and I saw both. So maybe "light" is the only thing I can measure. Most measurements involve a scientist looking at an apparatus or computer screen and inferring what it is that they're measuring. But maybe a blind and clever scientist could figure out a way to conduct all measurements using only their sense of hearing.
But in any case, can we even say the detection of light is well defined physically? How do we detect light? If we see an electron jostle around, for example, we assume that a photon must have made it do that (which is what happens in our eyes when we see.) But how do we know when an electron is somewhere? Maybe we send in a photon and see if it affected by the electron's presence. The whole thing is a chicken and egg. I don't think there's a completely satisfactory definition of what it means for something to be "measurable." Any sort of measurement requires context on the part of the observer, who has to understand what they're measuring just to carry out the measurement.
The only way out of it (not completely satisfactory) is to start with ONE thing you know is "physical." Anything that can change that "physical" thing (which one would call a measurement) would then be assumed to be physical too.