Personally i never liked the idea of the flagship on a game with this scale, they should just call it science/survey/exploration vessel. Surely every fleet has it's flagship? Does it really make sense for a huge empire (or the federation), to have ONE flagship?
It really depends on how you're defining 'flagship.' It is certainly the case that any organized collection of military ships will have one vessel which houses the commanding officer of the company, and which can therefore be considered the flagship of the squadron, flotilla, fleet, armada, or whatever else you want to call the group of vessels. It is also possible that there is a specific vessel in the fleet which is designated as the 'home' of the commander of the navy, or as the vessel which will fly the flag for ceremonial events, or which is the designated vessel for the use of a select group of VIPs (think something along the lines of Air Force One). Any of these could be considered 'flagships', not in the literal sense that they are the home of the commanding officer of a naval force but in the sense that they are the public face of the navy, at least on important occasions. I will of course grant that none of these definitions preclude there from being multiple flagships (in particular, aside from vessels of little direct military value, it makes little sense to have a specific warship always available for transporting VIPs or showing the flag on ceremonial occasions).
Another possibility is that the vessel has some sentimental significance for your empire - maybe it's the vessel with the original prototype hyperdrive, or perhaps it was built using funds provided by collection drives in schools. It might have no official significance, but for some reason or another the nation as a whole has a special place for it in the nation's heart. An example of such a vessel could be the USS Constitution, a wooden frigate from the 1790s which officially remains in active service with the US Navy despite having no real military value.
(i never understood why the federation takes so long to build ships / has so few ships when they have like a thousand worlds, but thats besides the point).
If we're arguing from an in-universe perspective, then perhaps the Federation feels that a larger space navy is an unnecessary expense. There are some indications that even full members maintain their own fleets, and to some extent the fact that the crews of the Starfleet vessels seen in the shows are largely human, especially in combination with the majority of the ships named bearing names related to human (and, often, specifically US) history, can be used in support of that idea. Additionally, from what is shown in the shows, the Federation is of at least comparable military strength to any one of its immediate neighbors, and possibly comparable military strength to combinations of two or three of its neighbors, aside perhaps from the Dominion. Without a clear threat from one or more of its neighbors, an extensive shipbuilding program is likely unnecessary given the circumstances in the preceding sentence, and possibly too expensive for the politicians to stomach.
Furthermore, most of the ships we see in the shows are on the high end of the scale - the Galaxy and Sovereign classes are certainly capital ships and the Constitution class is designated as a heavy cruiser. The Intrepid class is a specialized long-range exploration vessel, and so therefore can be expected to require more time than normal to design and build for a vessel in its weight class (which, at about a third the length of the Galaxy and Sovereign class, is probably analogous to a frigate or destroyer), nor would such a design be a top choice for large production runs except if the fleet is to be largely dedicated to exploration. The Defiant class seems to have been more overtly military than many other ships, and lacks many of the creature comforts that we see on other vessels; it is also by far the smallest full starship in Starfleet that we know much about, which indicates that it should be of a type that the Federation can turn out in quantity relatively quickly should such vessels be required, but which is likely to be neglected in peacetime.
And what if your flagship gets outclassed by a new ship design?
Flagships being outclassed by newer ships isn't necessarily a disadvantage; Admiral Spruance of the US Navy (World War II, Pacific Theater) frequently used the USS Indianapolis as his flagship, despite it being a cruiser of an older design when he could have used a battleship, carrier or newer cruiser. 'Most modern' isn't necessarily a criterion for selecting a flagship, and to some extent could be considered a disadvantage - after all, the most modern vessels are likely also the most powerful, which could cause problems if the commander decides that it's more important that he or she be at a different location on the battle field, as relocating would likely cause a significant shift in the power distribution of the fleet, whereas the relocation of an older vessel is less likely to cause as drastic a shift. There's also a question of which ships are most likely to suffer from degraded communications abilities or to be disabled soonest - that brand new battleship may have the best defenses in the fleet, but it's also intended to stand in the battle line and engage similarly heavy warships on the opposing side, so its staying power as a serviceable command ship might not be as great as a lesser vessel.
a free trade route is very overpowered early on, especially if trade research wouldn't be a prerequisite. Boosting production is nice, but would have your ship sitting at some planet instead of being out and about exploring and presumably becoming stronger. Science exploration sounds neat untill it happens on a big map and your flagship is 10 sectors away but you know the exploration will give you something you really want.
If trade will work the same way in GCIII as it did in GCII, then I'd say that sacrificing the flagship for an early trade route is almost certainly a bad idea. You lose the ship, you lose all the bonuses it can provide through exploring anomalies (some of which can easily amount to many turns of income from a trade route, especially the shorter trade routes you'd likely have in the early stages of the game, or allow you to dedicate a world's production to money instead of building another Defender), and you lose the ship that's likely in one of the better positions to continue exploring the map; all you get in return is a relatively stable bonus income and a relations boost with someone before the game has settled enough to determine who you really want to be friends with anyways, and who is likely close enough to be a reasonable first target. 100 bc per turn might be more of an advantage in the long run, but 1000 bc or a free warship now have a lot of things going for them, too.
I would also tend to object to a trade module on a flagship just from the perspective of if I manually order it to go somewhere and accidentally click a planet, I now have to remember that this isn't necessarily a ship that I want to use to form a trade route - early on, it's the only ship I have with a survey module, and even later into the game I don't necessarily want to sacrifice a medium hull ship that I can convert to some more powerful design just to get a trade route going.
I will also say that I dislike the idea of a ship which has the unique ability to perform a certain set of actions, especially if those actions are in any way actually useful. It's worse when you consider that flagships in GCII were irreplaceable (to a degree; you could certainly create a design which is in every way identical, but the game doesn't provide a way to produce more vessels of the flagship's design, at least not that I can recall) and could be bought from other empires; if flagships are given unique flagship-only actions that are actually worthwhile, then losing a flagship becomes more than a minor annoyance and completing the Naval Vessel Collectors' Set, Flagship Edition gains a value that just shouldn't be there for a glorified survey vessel with a unique name (at least, unless the player chooses to name another ship to 'Empire_name Flagship' or something like that).
