I use both and I started playing at the age of 7 in 1960 something

I was lucky to have a teacher that was open minded and we worked on both for the 2 years I studied with him. I find traditional grip best for my swing/bebop/jazz/New Orleans/etc. styles. I also think one could argue it's the best way to play traditional Jazz brush styles. I use matched grip for any Rock playing where I need to bash, but I also use matched for any Classical music applications. It also transfers nicely into timpani, although I use french grip (thumbs up) for that, and mallet keyboard instruments.
There are many great players that play one way or the other. One teacher I had said 'choose one grip and stick with it' (I never did!). I also remember an MD interview with the great avant-Jazz drumming artist Ronald Shannon-Jackson where he speculated that the right hand, which usually plays the time keeping function, is guided by the left brain, which is thought to be the mathematical side. The left hand, which in jazz provides a more interpretive and responsive role by 'comping' on the snare, etc, would be guided by the more creative right side of the brain. At least I think
the question about why he used a larger diameter stick in his left hand, but I think it also addresses the use of traditional grip in the Jazz tradition. For me, I just find it easier to swing when I play trad.
I usually start most students with matched grip.
I would also add that there are some incredibly skilled non-Jazz drummers, especially the recent explosion of double bass artists who can mix meters, polyrhythms, and four limbs with an incomprehensible degree of skill (at least to this geezer) and can still rock you into bad health (to paraphrase an old Jazz aphorism).