There's a distinct appeal to multi-instrumentalists, and jazz has plenty of them. Two who have had an impact on me personally are Tom Baker and Ade Monsbourgh.
Perhaps they were inspired in part by Benny Carter. Here is one of his early recordings on trumpet, away from his more regular alto sax. He plays with a solid technique and a clear sense that he is approaching the trumpet like a trumpet, not like an alto sax.
There are arguments against playing many instruments. For instance, the old cliche 'Jack of all trades, master of none' rings true all-too-often. Also, you have less time to devote to each of your instruments. Finally, there is the tendency for it be seen as showing off, which it may be!
Benny Carter transcends all argument and instead focuses on playing, not alto sax, trumpet or clarinet, but music. He is aided by other stars such as Chu Berry and Teddy Wilson.