> It feels more like the "pull in a 500MB framework instead of writing the function yourself" kind of simplicity.

Essentially yes, but it's a function that has been continuously optimised by engineers for 200 years.

We are still trying to solve the problem that we can't keep the plasma hot long enough to create fusion energy, so working on exotic conversion schemes is one step too far.

Consider also how complex these reactors already are, it makes sense to use the simplest method that we know works well.

In physics it is common to work explicitily with the components in a base (see tensors in relativity or representation theory), but it's also very important to understand how your quantities transform between different basis. It's a trade-off.

Yes, the L^p spaces are not vector spaces of functions, but essentially equivalent classes of functions that give the same result in an Lebesgue integral. For these reason, common operations on functions, like evaluating at a point or taking a derivative are undefined.

If you care about these you need something more restrictive, for example to study differential equations you can work in Sobolev spaces, where the continuity requirement allows you to identify an equivalent class with a well-defined function.