This is the key point. I'm assuming that it downloads the update and then waits for me to agree to install it, but however it works it doesn't interrupt my browsing while I'm in the middle of something.
This is how Mozilla's own updater works (if you use the .tar.gz version), but the distro package updater just overwrites everything without waiting and applications like Firefox have no control over that. As a user, you'd really want to disable unattended updates for such software.
It's not an issue for these .deb packages because they enable the (experimental) forkserver.