Yes?Would it have really hurt them to put actually Hull Armor on the Galaxy's instead of relying on shields. I mean you would die of Alcohol poisoning if you take a shot every time the Enterprise Ds shields dropped during combat scenes. They forgot the one rule of Empires (And yes the UFP is an Empire as much as they hate to admit it) Your Flagship needs to be a beast of a ship that can not only deal damage but take damage as well. Thankfully they sidelined that Brahams lady and her team and got in some real Warship Engineers to create the War Galaxies and the Galaxy Xs. But it took the Dominon anal raping the Odyssey to cause that change.
I get a lot of folks here thinks Trek ships are poorly designed, but it's really telling in setting that NOBODY seriously up-armors ships. Not the Klingons, not the Romulans, not the Cardassians, not the Dominion... NOBODY does it. They all similarly depend on the combination of Shields+SFI just like the Federation does.
This fundamentally means that within setting there must be some logical reason nobody does it. It's not been explicitly stated in canon, but I can think of a few logical reasons off the top of my head.
1. The tradeoff to acceleration and maneuverability isn't worth it.
It may be that more hits are evades by evasive maneuvers (which we see called for ALL THE TIME in Trek) and that adding armor to the ships would make it so that those maneuvers are dramatically less effective due to the Impulse drive and maneuvering thrusters having to accelerate so much more mass (as any serious amounts of armor on the ships is going to add considerable mass, given that you generally need fairly exotic high density materials to effectively armor against Trek weapons).
2. The materials needed are prohibitively expensive for large scale deployment.
As noted above, armor for Trek ships tends to be required to be made of highly unusual materials for it to be effective against Trek weapon systems. Think things like Neutronium and other exotic matter. These are things not easily replicated (as we know exotic materials often have difficulty being replicated) and thus likely take considerable investment in. This means that for large scale production lines like the Galaxy class it simply may be to cost prohibitive to manufacture the amounts needed.
3. They do not have effective armor materials at the time.
I'll grant this is a variant of the point 2, just coming at it from a different angle. It may well be that they simply do not have effective armor technologies that work against common weapons technology at the time, and so it's kinda pointless. This seems weird? Consider most of the 18th to 20th century re: armor for infantry, it wasn't until the late 20th century that we developed materials that were effective against the weapons in common use, Trek might be in a similar situation.
Further, no amount of armor would have saved the Odyssey. F=MA and Dominion fighters have a shitton of both. Plus, as I noted elsewhere in thread, the ship was rammed right in the main anti-matter storage area. Adding armor wouldn't have changed a damn thing.
Finally, it bears repeating that there's no such thing as a "War Galaxy" that was an idiotic bit of fandom dreamt up by SB, and the Gal-X is also not truly canon, though it's closer to being canon than War Galaxies ever were.