By research, do you mean academic research?
Universities do research on usability engineering (I considered that when I finished my last degree, but the fees did the first of the two big jumps in the UK that year, and as I was doing it for fun, I thought it too costly a hobby degree.). It's been done for many years.
Accessibility research, I suspect, is not as common as usability research. For usability, you can use a sample of test volunteers by advertising "help my research, earn £5 / $10" and get a fair number of low cost volunteers. For accessibility research you need a set of volunteers with specific needs / abilities or lack of abilities. Also, in usability engineering, you are doing research where you yourself may be able to spot an engineering problem and go for it as a side project to your main work, but with accessibility, there are a smaller number of researchers with a disability themselves, making it harder for the average researcher to spot new problems of accessibility themselves. (Unless they have a relative or friend with a disability who complains a lot to them - I knew a lecturer in this situation, he could test things on his relative or ask if they thought something was likely to be a problem.)
I've read accessibility research papers where they tested on five or seven people. I've read usability research papers where they tested on 20, 40, or more, which makes it easier to prove your research / solution is valid. And researchers like to know if their work is correct.
PS Sites offering Usability consultations could easily be run by individuals like me who read up on things and then just sort the most obvious usability problems - tiny text, low contrast text vs background, bad placement of items, silly animations on the home page, too many steps in a process, too many font faces, bad use of colour (all genuine problems, not snake oil at all). Only a few I suspect would be run by people with a research background in usability engineering, and their fees would be rather high, and they would be used by big companies where a lot of money could be gained by improvements, and not used your average 10 - 20 page site.