A good player will always sound good. The gear does not matter. A good player will also play and sound beautiful and inspiring under the worst circumstances.
I've had to borrow enough gear in my life that I can disagree with you here, at least to some degree. You're much too casual with the word "always".
My worst circumstances: borrowing a bass full of large cracks and open seams, with no sound post and 50+ year old strings. Playing that, I definitely didn't sound beautiful and inspiring. It was more of a stage prop than a musical instrument. True story.
That's obviously beyond extreme, but if we accept the premise that a completely ruined instrument will completely ruin a player's sound, then you must also accept that you lose something when the gear isn't functioning properly. It's a matter of degrees.
To answer OP's question: let's compare a $50 fiberglass bow with my favorite Boris Fritsch bow, which costs about 100x more money. Let's even say they both have fresh, high quality hair, and everything else is working correctly. Do I sound 100x better with my Fritsch? No, of course not. Money and value is an abstract concept and these things don't scale like that.
So why did I spent 100x more money on a bow? Because it
feels 100x better. The problem I have with cheap bows is they require so much finesse and effort just to get a decent sound and articulation out of them. Some strokes simply don't work. There's a limit on how far you can push them, dynamically. One constantly feels like they're fighting with the bow. It's annoying, and after some time it becomes depressing.
A great bow has the opposite effect. It will feel like it's doing all the work for you. It responds perfectly to everything you do, and gives you complete control over your own sound. It's a positive and empowering experience. That extra money certainly buys a higher quality sound, but the real payoff is in confidence. When I know my equipment is working optimally, I play that way.
I just don't have any fun playing instruments that don't feel right. And if I'm not having fun, what's the point?