Yes, and I'd take it further. What I'd like to see more of in physics texts is presenting a problem
before offering the solution. Too often you get what amounts to a laundry list of techniques and ideas, which are the components to the answers to hard problems, but the student isn't motivated to learn them. If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill. For example, I think calculus is probably better learned
after trying to write down some force laws, and perhaps doing some numerical analysis. Then when you learn them you realize those nice closed-form solutions aren't busywork, they are
huge labor saving tools that eliminate ad hoc labor intensive analysis.
I would also deemphasize the more mathy parts of calculus - do you really need a deep dive into continuity or the fundamental theorem of calculus? Eventually, yes. But it's just like programming: you're not going to need to understand language theory or ADTs or category theory or lambda calculus to write your first program. Or your second. And, IMHO, you should only reach for this understanding when you realize you need it. Otherwise, it won't integrate well into your toolkit.
I would also deemphasize the more mathy parts of calculus - do you really need a deep dive into continuity or the fundamental theorem of calculus? Eventually, yes. But it's just like programming: you're not going to need to understand language theory or ADTs or category theory or lambda calculus to write your first program. Or your second. And, IMHO, you should only reach for this understanding when you realize you need it. Otherwise, it won't integrate well into your toolkit.