But it's certainly not the study of what mechanical computers can do. Among other things, mechanical computers all have bounded resources unlike Turing machines.
Nobody is saying that's not important. But the field as a whole began before mechanical computers were invented or practical, and there are several subfields that are basically indistinguishable from mathematics.
In any university, Chemistry is not the study of beakers nor is astronomy the study of telescopes.
Both Software Engineering and Computer Engineering exist, as sub-disciplines, but it doesn't make sense to argue that somehow studying Graphene (a chemical which exists) is Chemistry while studying non-blocking algorithms is only Applied Computer Science somehow just because such algorithms could be used on an actual computer.
If N is sufficiently (polynomially) large, the two are approximately equal.
Yup, so do humans with paper and pencil.
Also if you ever work with the turing machine (NFA hooked up to an infinite recording tape) it is not at all "intuitive" that this construction comprehensively captures the world of computation.
Harold Abelson points out in one of his lectures [0] that computer science isn't about computers any more than biology is about microscopes.
From that perspective, it is clear that Turing found an existing discipline of computer science and made major contributions to it. But it doesn't really seem right to say that he invented or founded computer science.
[0] https://www.youtube.com/watch?v=-J_xL4IGhJA&list=PLE18841CAB...