Kasparov is fond of this quote "every Russian school boy knows... [x,y,z chess strategy, trick, opening move etc]". But there was a time when they didn't know. In fact tere was a time when even the best players didn't universally know such stuff. So, I think that's where these old masters and old games are an interesting learning experience (I also like the history, but that's an aside).
In modern games there's just so much subtext that you don't know. In these old games, however, that subtext often comes to the surface -- it was all new back then. So studying these games gives one a more ground up learning experience.
Always use modern resources to you advantage though. Find a modern book on Morphy and let your engine have its say also.
PS, I think the best era to learn from is probably the 1930s' through the 1970s'. It was balanced between more sophistication and technical skill than earlier and yet fairly clear boundaries between playing styles and the play was so not concrete (usually) as to not be able to follow the principles behind the moves.
After winning the first American Chess Congress in 1857, Morphy spent 1858 in Europe. He beat all comers—convincingly. I believe the one player he didn’t beat was Staunton, who was past his prime and who ducked all offers to play Morphy.