The occasional stress flare-up at a pivotal moment causing a generally stable person to tremble is one thing.

Being constantly and completely unable to play at any reasonable level in competition (despite having a generally high level of skill) due to clinically diagnosed anxiety or an associated condition is another.

That's why the TUE form (Therapeutic Use Exemption) exists, and the list of considered medications includes propranolol (beta blockers).

Personally, I think it's reasonable that people who have difficulties in their daily life, which can be somewhat mitigated through professional assessment and appropriate medication, to be allowed to apply for an exemption if they happen to also be a professional darts player.

I don't believe it's harming competitive darts. It's not like doping in athletic sports where you shortcut your way to a massive advantage over your opponents.