To be fair, choice would be to allow both in your JSX like Preact does. Usually I wouldn't bother as I get your point with consitency. But from a practical standpoint, whenever you paste some HTML code from somewhere else, the first thing I need to do is search/replace class= to className=. Probably more relevant for tailwind/bootstrap users than MUI.
That's true, but there are various other syntax differences that mean that pasting HTML is always going to require some fixing up. For example, JSX requires all elements to have closing tags or use the /> syntax, whereas HTML has elements like input or img where's that's not correct.
That said, "class" shows up a lot more in most html than "input", so I can see the advantage of being consistent with html there.