As the title suggests, I think it would be a great way to manage large armies, especially for newer players. So you can easily organize different types of units. Or maybe there could be some way to set a factory to put all units spawning from it into a control group. Sorry if this has already been suggested, but it was suggest that I suggest it here after asking around if you can do this in the game as I am still new to this game.
Click on one of the unit you want, then double click the selection icon bottom left. This will select all units of that type. Alternatively, ctrl+z will by default select all units matching your selection on the screen. If you wanted all of a broad type of units, for example all land combat units, you can do that by default with ctrl + shift + F7. There's key combinations for factories, fabbers, combat units, all units, on screen or everywhere. You can see the key combinations (and change them if you like) by going into settings, on the keyboard tab.
I most of the time use Shift + Fx to select my units. Thing is, I'd rather to have like the OP suggested, factory of a kind set to a group, and all unit spawn from that group selected when recalling that group. I already do it (setting factory to a group), in fact, to quickly handle rally points (most of the time) or changing queue (rarely). Issue is that with (Ctrl +) Shift + Fx, in share army games, your mate is going to be pissed when you take control of his unit involuntarily
