Potential General Model of Computation with Physics?
It would be meaningful, if you properly defined "formal physical system", "set in motion", and so on, in a mathematical way. Pretty much anything can be made meaningful in mathematics (which is what this sort of theoretical computer science really is).

The question is, is it useful?

It would seem that the functions computable by Turing machines are a subset of this new class, since you can make a Turing-complete physical computer with enough rolling marbles. (Or, if you allow transistors in your "formal physical systems", I could just use "my laptop at the moment when I run this Python code" as the system.)

Then, are there things your physical systems can do that Turing machines can't? Given that a Turing machine can simulate classical mechanics to arbitrary precision, given enough time and memory, I'm inclined to say no.

Finally, are your physical systems easier to work with mathematically? The answer seems like a pretty solid "no", given how much calculus is involved in classical mechanics, compared to the simple state-machine-plus-memory of a Turing machine.

So while you could in theory use physical systems to define computability, there doesn't seem to be an advantage to doing it this way.