You're talking about applying tree search as a form of network architecture search (NAS), which is different from applying it to LLM output sampling.
Automated NAS has been tried for (highly constrained) image classifier design, before simpler designs like ResNets won the day. Doing this for billion parameter sized models would certainly seem to be prohibitively expensive.
Fair enough - he discusses GPT-4 search halfway down the article, but by the end is discussing self-improving AI.
Certainly compute to test ideas (at scale) is the limiting factor for LLM developments (says Sholto @ Google), but if we're talking moving beyond LLMs, not just tweaking them, then it seems we need more than architecture search anyways.
Automated NAS has been tried for (highly constrained) image classifier design, before simpler designs like ResNets won the day. Doing this for billion parameter sized models would certainly seem to be prohibitively expensive.