Is it? On Linux, you can overwrite the file, but the underlying inode will still be open, and the 'invisble' old version will linger around - you don't have any easy way short of restarting everything to make sure the new versions are being used.
And with Chromium this directly leads to crashes - when you update the browser as its open, the new tabs will open with the new version of the binary, with the old ones still using the old binary - which usually leads to crash.
I prefer 'you cannot do X' instead of 'we allow you to do it, but it might misbehave in unpredictable ways'.
I don't use Chromium. I never had issues with Apache, MySQLd, Firefox, Thunderbird, ... . You can even swap out the Linux kernel under userspace it still keeps all running.
> maybe programs shouldn't be allowed to update themselves.
Honestly I'd be all for this if the OS had a good autoupdate mechanism for 3rd party applications. But that's not the world we live in. Certainly not on windows - which is too busy adding antivax conspiracy articles to the start menu.