Older works keep older instruments in use among professionals and amateurs. You may not have any visibility of the early music community, but there are quite a lot of us and we're out there playing recorders, viols, baroque flutes and oboes, baroque violins, harpsichords, clavichords, hurdy gurdies, musette du cour, rauschpfifes, racketts, shawms, sackbuts, cornets and the list goes on and on.
During the 20th century a revival happened in early music, and the idea of historically informed performance gained a lot of traction. But to play music as it was originally meant to sound means you need instruments which can produce those sounds, so a lot of very clever people have spent a long time trying to make instruments which can do that, while other very clever people have tried to figure out what the performance technique was for these instruments based on written sources. Regrettably without a time machine we can't hear the original performances of Vivaldi or Handel to know what they sounded like to the composers, but we can come up with things we like that have some evidential justification.
That said, old music is also often played on new instruments, often very badly. Pick a random recording of Bach's keyboard music for an example - you're probably not going to get one of the good ones. Sometimes it can work to use a modern instrument's capabilities to enhance a performance of music that was written before anything capable of that was ever built, but more often you unfortunately end up with someone who only really knows how to play music written in the 19th century trampling all over some Bach and making it all mushy.
It can work though, and there are recordings out there of people who've managed to pull it off, sometimes using completely different instrument families to the original but still capturing something very wonderful in the performance. Musicianship and understanding are most definitely required.
Oh also, go to a gathering of folk musicians and ask them if the hurdy gurdy is obsolete. I dare you. Especially in Hungary.