Lots of people don't want to play in the Eastern European basketball league. They specifically want to play in the NBA. It's not about basketball, it's about the perks.
Sidenote: Other than the height, the absurd athleticism and skill at shooting ball are grown over a long period of hard work. Nanotechnology cannot substitute for hard work and years of learning the strategies and techniques of playing the game...
Of course it can. You don't even have to go nano. Give me a team of people from Boston Dynamics for a year, and I guarantee you they'll be able to make me a wearable exoskeleton that is better at throwing the ball on-target than the best NBA player.
It's just, like GP said, with such tech allowed, "the entertainment and spectator aspect would fall away". Sport disciplines are designed to ensure scarcity of good athletes.
That's partly true, but there are other dynamics at work as well.
Expert sewage/waste management workers get paid a lot less than those trades, though their trade is necessary and involves lots of sacrifice/job unhappiness.
On the other hand, private military contractors and undersea welders make a premium, despite being nominally "service" or less popularly lauded jobs.
There are other factors at work in addition to this.
And medicine, finance, and consulting, require a fair amount of intelligence and the barriers to entry are high, keeping wages high.
I don't think this is ever going to change in human society. If a job is fun to a large group of people, then it will pay poorly because many people will want to do it. And poor pay decreases the satisfaction one gets from such a job.
The only people who win here are those who find a job fun / satisfying that most other people cannot handle.
There's a reason professions like doctory, investment banking, and consulting pay so much, they involve lots of sacrifice and/or job unhappiness that you have to pay people a lot to get them to commit to the job.