Think about this a bit. Contemplate what happens if you use sftp, vscode remoting, or anything else nontrivial. Hint: “cloudflared access ssh-gen” is not actually any sort of proxy, and the ssh -tt command is a kludge that should, if openssh were more on the ball about inherited file descriptors, should not work at all.
The right way to to this is to use Match … exec. Or to ask openssh to add an option for a command to execute before reading IdentityFile. Or to ask for an IdentityFileCommand option. Or to use a custom ssh agent.