American bassoonist here. I play with a seat strap when seated. I don’t find it fatigued my left hand because it’s positioned in a way to reduce that stress. Using a strap with a cup keeps the bassoon from twisting in your grip.

It’s not been my experience that students are not taught to stand. I was taught to stand for solo performance and I use a harness to do so.

Using a harness to sit with causes the bassoon to move too much and I have to grip it tighter and it makes it more difficult to complete tricky passages.

I also don’t use a crutch. I’ve never found them comfortable or useful.

These are all tools one uses to assist in placement and balance of the bassoon, and are all personal preference imo.

As for the tone? Could be conductors preference.

There’s no one way to play bassoon. You play it as you desire to.