This is discussed in some detail in TWiV[777], a discussion with Ron Fouchier. If you use influenza as a model, the picture looks completely different - new strains are coming up all the time and outcompeting the older ones, but that's just because people have developed immunity to the older ones (antigenic drifts). The new ones are not fundamentally different or more transmissible. For people who don't want to listen to the whole thing, the main point is also made in a NYT opinion piece[2].
Pueyo claims that alpha is 60% more transmissible than ancestral type, but again the evidence doesn't strongly support this. Indeed, a preprint just came out[3] in which alpha looks pretty much identical to ancestral type when it comes to viral loads and clearance.
I've really enjoyed and appreciated Pueyo's writings. In particular, I think "The Hammer and the Dance" was groundbreaking and we could still learn the lessons from it. But I think this one is a miss: it could present real insight, but instead mostly propagates conventional thinking.
There's a really interesting science communication aspect to delta: it's basically a proxy for the (very true) statement, "the virus is still dangerous." In fact, one prominent evolutionary biologist accused the NYT op-ed of verging on "delta denialism". Accurately communicating reality in a way that is useful to people is fantastically hard, and we just don't have an ecosystem for it. I think this is the reason I've become addicted to TWiV and other similar highbrow sources - I hate being fed partial information and feel compelled to learn more.
[777]: https://www.microbe.tv/twiv/twiv-777/
[2]: https://www.nytimes.com/2021/06/27/opinion/covid-vaccine-var...
[3]: https://twitter.com/BallouxFrancois/status/14149092626571141...