That is why we should get rid of setuid binaries. GrapheneOS does not use them and was therefore not affected. On the desktop there is also a project called Secureblue based on Fedora Atomic that is moving in a similar direction and has already eliminated a large number though not all setuid binaries. As an alternative to sudo, su, and pkexec there is for example run0, which is available in distributions using systemd. Since systemd 259 there is now also the --empower parameter which like sudo elevates the privileges of the regular user. Essentially any distribution could start removing sudo and create an alias so that users don’t have to adjust immediately.
No, it is not affected by the exploit as presented. This is a page cache write, so writing to a binary that root will run later can work too. This isn’t a reason to push an agenda that dislikes setuid binaries.
That would only work if the user had access to a binary that they wanted to run as root. Ideally this shouldn’t happen at all for most users. There is almost never a legitimate reason to run any program as root unless for example it is a service that absolutely requires it. In Fedora based distributions SELinux also prevents systemd from running any binaries or scripts that the user has access to as root. Removing setuid binaries and strictly limiting features like user namespaces through SELinux would make Linux significantly more secure. It’s absolutely ridiculous that even an outdated Android smartphone is more secure than the average Linux distribution these days.