I agree with this. For example, teaching Lie groups / algebras from the historical perspective of the problem Lie was trying to solve would be a tedious exercis

I agree with this. For example, teaching Lie groups / algebras from the historical perspective of the problem Lie was trying to solve would be a tedious exercise in multi variable calculus and PDEs. On the other hand, once you have a sense for the abstract and how it’s used, going back to read Lie’s original work (there’s a translation my Merker) gives interesting historical perspective, context, and new understanding. But I wouldn’t want to learn it from that perspective.