Yes, I think captchas are the wrong solution. They annoy all clients, humans included.

IP+subnet based throttling on the other hand is a perfectly working solution, optionally with a proof-of-work or login requirement for intensive POST requests only. Why is it a problem if only a few requests per day are made per home IP? Just how bad and inefficient is the web server?

Bots are not a second class client. They were here before AI, and they, like AI, work for humans. For the most part, they're not trolling the web autonomously.