I guess my question is how many is enough? Teaching a spin and recovery
once? Teaching it 10 times? Teaching it 100 times?

I don't know. How about until the student gets it right?

Or is it sufficient to simply teach spin avoidance? What causes
a spin and how to not do it?

No. What usually causes a spin is inattention. When a student is
concentrating on a maneuver in a canned situation, you cannot possibly
simulate the circumstances that will lead them to a spin entry, that moment
of confusion when nothing seems to be working right and then a calm
recovery. There are some counter-intuitive things that must go on and they
must be taught, not talked about.

How much should we focus and teach spin avoidance vs. spin proficiency?

Not spin proficiency. We are not aerobatic pilots. Spin recovery.

When I was getting my helicopter license, I told the instructor that if we
didn't do autorotations to the ground, I would go shopping for someone who
would. In that manner, I learned before I needed it the very critical timing
required to pull it off. If I had had to guess how to transition mentally
and manually from an auto to a hover to an auto to the ground and had to bet
my spine on it, I very likely would have lost the bet. I am a firm believer
in instruction to prepare the pilot for whatever he/she may face. If we face
spins, then train us how to get out of them.

I already know how. If nobody else wants to teach it or learn it, I
shouldn't care. So I won't.