A mobile app was requested by many people before Peter joined OpenAI. Also the App Server was in place for the desktop app well before that too. See https://openai.com/index/unlocking-the-codex-harness/ for some history.
That was my thought too. Claude Code and Codex are very close to Claw already (general purpose computer use) and moving increasingly in that direction (mobile integrations, built in memory features etc.)
The main issue is reliability, so I think the corporations are going to take a much more gradual, piecemeal approach, and probably end up with something like Claw within a year.