Thanks for the thoughtful response. I think maybe my objection to MY curriculum was being handed a lot of mathematical tools which I didn't need, and so it was impossible for me to "slot them in" to my toolbox. Most named solutions to differential equations were just like...why? (e.g. Bessel functions, or Green's function or...). I think it's a failure of pedagogy - I personally think you should give students the problem before giving them the solution. But the physics curriculum seems to want to give you solutions first and then tell you how you can use them. My brain doesn't work that way; tools fulfill a need. It would be like teaching a carpenter all the ins and outs of every tool in the shop, without ever building anything. How is the student supposed to organize that knowledge? Alphabetically?

I suspect that, just like how algorithms rarely pop up in software practice, so too do these kinds of tools pop up in physics practice, and when they do you probably get that same happy jolt of "Hey I finally get to apply this knowledge!" And that happens about once every 2 years.