Yes, I've seen a few comment about tyre availability been limited, whether its all sizes or just some I couldn't say, but I wouldn't wait until you're on the edge as its not a drive up and get replaced type thing.
Some tyre places won't fit anything other than T0 (Tesla certified) tyres, In coming up to 6 years I've never felt the need for a puck, the underside is way stronger than the underside of the average ICE and how many people complain about a tyre place piercing the floor of their ICE? (Care is still needed but they're not exactly delicate). Tesla are about 50% more expensive for the same tyre as buying online
As for alternatives, tyrereviews website is an interesting read but you need to check the sizes. I think they now ship with Pirellis and they're not thought to be as good as the Michelins, but ask 3 nerds for their favourite tyre and you'll get 3 answers.