In a given orchestra (for example), what instruments have fixed tuning? A piano yes (although lots of orchestral music doesn’t have piano.) The harp? I struggle to think of others.
Wind instruments essentially have continuous tuning because the player can adjust the pitch with their lips and vocal shape. Orchestral string instruments are all fretless (and thus continuously pitched.) Singers, same thing. Even fretted instruments are often played with a lot of vibrato that masks any true pitch problems.
I think the inability to play with a perfect pitch is more the exception than the rule (at least in “classical” music), it’s just that piano is such a popular instrument in the modern era that this becomes a problem.
Not that many: the piano, the harp, the glockenspiel, etc.
But the thing is, most modern music, is not with a classical orchestra, but can still have violin (and in some genres, like bluegrass, irish, country, etc. it often does).