You can use something like OpenRouter, which lets you access essentially all commercially available models. Including open-source models. There are no rate limits.

You pay a different rate per model (OpenRouter shows the pricing transparently). You load your account with credits. I use it daily (undoubtedly far more than the average user) and loaded 50$ with credits five months ago, but I still have over 1/2 of it left.

I think it is hard to believe that Kagi would be any cheaper and have no rate limits.