I tend to think the same way, though I have no consistent idea as to how that would work. I just know that having thousands of distinctive insignia is being a little silly. One thought I had is that the Enterprise delta could represent UESPA, which was the operating agency of the Enterprise and would be consistent with it's appearance on the Friendship One probe.
The Constellation's I suppose looks somewhat Vulcan so it could have been under the Vulcan Science Academy, or whatever replaced the High Command.
It might be a nice way to show that at this point in history Starfleet is still in an embryonic state, in that it may have absorbed the old institutions like The Andorian Imperial Guard and the Tellarite Exploration commission (yes, I made that up) but it still have all the infrastructure and some of the trappings of those older organisations.