To elaborate, because I don't think some of the people reading this understand the reason, typically a lot or most of the cost in "agentic" API usage is cached read + generation. Cached read costs scale with turn count, which multi-model switching doesn't increase, and of course generation gets cheaper if you do some of it with a cheaper model. When you switch models the "catching up" batch of messages is just a single prefill and then that goes into cache. You don't even need to have the same chat history across models so long as the view from each model's perspective looks like a series of appends.

The main problem with model routing in my experience is that to work well the router needs to be pretty strong, maybe even moreso than any of the actual models in service. There are probably clever solutions to this but I haven't seen any that look better than just using sub-agents.

> which multi-model switching doesn't increase

Given model A with cache C(a) and model B with C(b)

Isn't this not true because the moment you switch models from A to B, you need to provide C(b) the latest conversation diff since C(b) last updated, say many turns ago?