The catch is ollama cloud is likely to increase prices and/or decrease usage limit levels soon. Free tier has more restrictions than their $20/mo tier. They claim to not store anything (https://ollama.com/cloud) but you'll have to clarify what you mean by "private" (your model likely runs on shared hardware with other users).
I agree. "Free" usage could mean tradeoff. But for side-project and experiments, to accesss open source model like gpt-oss, as my machine can not run, I think I will accept it.
My experience with the free tier and qwen3-coder cloud is the hourly limit gets you about 250k tokens input and then your usage is paused till the hour is up. Enough to try something very small.