Idk, I probably haven't used Debian derivatives long enough, but isn't installing random .deb-s somewhat of a bad practice? I mean, repos exist for a reason (ignoring the fact they usually have like 3 packages in the official repos)
A lot of software wont be distributed with a PPA to add.
Additionally, debs are useful for offline installations, with apt you're able to recursively download a package and all of it's dependencies as deb files, then transfer those over to the offline machine and install in bulk.
That being said I've never had great luck with the software center, it's always felt broken. I'll typically just dpkg -I <pkg>.