The general idea is that Anthropic/OpenAI is pushing this narrative as an attempt at "Regulatory Capture"[1] which would allow them to make it prohibitively expensive for anyone but them to enter the market thus stifling competition.

* 1: https://en.wikipedia.org/wiki/Regulatory_capture

> Please explain how putting an upper bound on how good the strongest models can be prevents cheaper less strong models from catching up, rather than enabling it. I do not understand this argument at all.

They are not proposing to regulate only the strongest models. They are proposing to regulate all models. If they are already on top, regulation may stop them from proceeding further, but it also stops the cheaper alternatives from catching up.

If they feel they have reached the asymptote of the curve, then regulation doesn't affect them, it affects those who have yet to reach the asymptote.

I don't think "putting an upper bound" was OPs phrasing?

That’s not the argument.