This is not really fixable until you get an Ubuntu Core Desktop iso. The updater handles Debian packages as well as snap updates, while the Ubuntu Store is exclusively aimed at managing snaps.
The other one is for handling update configuration for the deb part of the system. Now if you had a desktop iso exclusively based on snaps, then presumably you would be able to manage everything through the Ubuntu Store.
In that case, it may not even matter since snaps are automatically updated by default. You would only see a notification to update to a new version of the system, at most.
We are still probably a year or two from a snap-exclusive Ubuntu iso though. Until then, all three applications are necessary.