A few ideas to consider:
The Enterprise-D may have been atypical of other Galaxy-class ships and that her duties as the Federation flagship required her to stay closer to home than other vessels of the class (I could see many Galaxy-class ships being recalled home during DS9's Dominion War though).
Exploration may also not be limited to just new planets and star systems, but investigating anything unknown, including things in Earth's own backyard. "To boldly go where no one has gone before" could also mean confronting strange things that pop up well within Federation space. It need not be always taken so literally, IMO. And given the vastness of Federation space, it's plausible that even well-charted sectors may contain occasional new mysteries.
Another possibility is that the Enterprise-D was still a relatively new vessel even by Season 7 of TNG and still just in the first phase of her operational lifetime. Maybe the upgrades we saw to the ship's bridge and elsewhere in Generations were in preparation for a long-term deep-space exploration mission that she unfortunately never got to embark on after Veridian III.
Yeah, except that Star Trek refuses to use the term flagship correctly. The US Navy does not have one fleet, it has several. Each fleet has a flagship that carries the commanding admiral of that fleet. And if I recall correctly, that is not the same of the commanding officer of that vessel.
So this entire 'the Enterprise is the flagship of the fleet' is just something that never vibed with me.
Now, I can understand that perhaps they wanted a ship with the name Enterprise closer to home, because that somehow carries weight, but it is still a huge waste of resources to use something that is capable of staying away from anything remotely considered nearby Federation space for I believe it was a decade on errand runs that could have been done by many other vessels.
Only in fiction is the concept of one ship being cool to enemies important in diplomatic relations.
Hell, let's say in a fictional sense, the US Navy sends the Enterprise and its support fleet to lay wast to a part of Russia, and THEN think that sending an ambassador over on that ship because the Russians will respect that.....
Your second reasoning is fair, but again, those duties can be done by ships that still need a reliable support network. Again, the idea of the Galaxy class was and is that it doesn't. So again, waste of resources.
Your most fair point is really war. Even though is it a true explorer, its firepower is insane! Having about 10 of those with a support fleet of about 40-60 other ships.... Hell, an Excelsior can be upgraded to pack a real punch as seen in season 4 of DS9. So yeah, that is still the most fair point for keeping Galaxy's classes close by.