No, only Anthropic has that policy (and I think even that is relaxed for an unknown period if you use the Claude Agent SDK: https://support.claude.com/en/articles/15036540-use-the-clau...).
OpenAI, Kimi, Qwen, GLM and Deepseek all allow it.
I'm not sure about Gemini.
The opposite, how easy it is nowadays should be clarified. Codex's app-server quite literally is built to be integrated with, authentication is a breeze and it's quite stable, compared to the TUIs that are around.
It's a real shame Codex is moving in the direction of hiding stuff on local disks from users, hopefully they're revert the decision of encrypting the agent>sub-agent prompts so we get back introspection again...