Sorry, but Marth has gotta be there. He's appeared in the most FE games and is the OG protagonist. He's also easily the best representative of FE protagonists as a whole, since most of them are on-foot sword wielders and Marth fits the bill for the archetypical lordling personality and backstory. I'd also argue that he's the de facto face of the franchise; there's a reason that Marth was tied into Awakening more than any other "legacy" FE character. Also, Sakurai said he wanted to add Marth as a second sword character in Smash 64, not Sigurd. I like Sigurd and think he would be a good choice, but he would have to be in addition to and not instead of Marth. I'll even go a step further and say that Marth's moveset is the single best representative for the Fire Emblem series as a whole that I can imagine. The whole theme of Marth's moveset is spacing, which is incredibly important to Fire Emblem, a tactical role-playing series where you need to position your units in just the right places to take advantage of the enemy. It's actually pretty amazing how Sakurai was able to translate the feel of a strategy-focused game into a platform fighter. I suppose that another FE on-foot sword user could hypothetically use this type of moveset, but there are few at best that make sense for this kind of play as much as Marth (it'd be weird for Ike to do it, for example), and certainly none with more credentials than him in terms of legacy and importance to the series. If we only got one FE character, it'd be Marth, hands down. The only points against him are lack of recency and not being the absolute highest in popularity, though only a few FE characters are going to have recency on their side at any one time and Marth certainly isn't a slouch in popularity. His current popularity also speaks to his great legacy within the series.
Source for Marth being planned in 64:
https://www.sourcegaming.info/2015/12/13/sakurai-fe25/
According to Sakurai, it seems like Marth would have been in Smash 64 had there been more time and/or resources.
"The Marth Remakes besides FE12 were terrible." So just Shadow Dragon? That was the only "Marth Remake" other than FE12. I guess FE3 technically includes a remake, but it also includes a whole new story afterwards.
With Hector, I'm down for a FE7 rep, but I think it ought to be Lyn. I also don't think that just being an axe user is enough; for me, Ike is essentially what would be our "axe wielder," as he plays fairly similarly to how I'd imagine Hector, minus potential thunder effects (which I don't think would be super prominent in Hector's moveset). Lyn is my number one pick for a FE character that isn't already in the game. She's absurdly popular, only really outranked by Ike. Also, FE7 is an awesome game and could use representation. Yes, she's a sword user, but I don't care about that. Give her a bow for a special move, some throws (like how Fox uses his blaster for throws), and maybe a couple of aerials (like Villager's slingshot) if you really care about new weapon types.
As I already tangentially covered, Ike is there primarily because he's ridiculously popular in both the FE fanbase and the Smash fanbase. Besides that, he's also a really good contrast to Marth in terms of gameplay, personality, and story. If you really and truly care about new weapons, then you could insert the Urvan into Ike's moveset for a few moves, but such a change would have little impact.
With Black Knight, I don't view a villain as an obligatory thing for each franchise. BK probably is the most iconic FE villain, but there are other FE characters that are not villains who are still more iconic than him. Plus you could sort of count Robin as a villain if you changed his Final Smash. I have a lot of good things to say about the Tellius games, but I don't think we absolutely need another rep from them, though I wouldn't have a problem if we did (I'm trying not to let my bias come into play too much here). While I think BK could be unique and interesting, I don't feel like he has enough else to warrant giving him a high priority. I was alright with an AT for BK.
Robin with alts is an interesting idea but I don't know if you could represent everybody properly like that. That one leak had Soren based on Robin and we *almost* bought it (lol how this fake text leak keeps coming up), and a lot of these characters use Staves upon promotion, but this would be admittedly hard to do well. For example, Soren and Lewyn are focused specifically around wind, while Micaiah would want a Sacrifice mechanic to fully represent her and Celica would want a self-damaging mechanic. In retrospect Robin was a pretty good choice for the Awakening rep, and he's nowhere close to the same as the other sword users.
Lucina's an easy Echo; she's also very popular and plays an important role in a game that was huge for the series as a whole. I like her being there more than Chrom.
I'd really like to be able to argue more in favor of Ephraim, as Sacred Stones was a really enjoyable experience and Ephraim is an awesome character in a lot of ways, but I'm not inclined to include him just because he has a lance. And I'm not sure that Sacred Stones was an important enough game to warrant a full PC. Don't misinterpret me; Sacred Stones is among the FE games I've played for a lot of hours, but I'm trying to be mostly unbiased here. I wouldn't be disappointed with Ephraim, though; he's a real cool dude.
Roy is an odd duck. He's really popular but a lot of that is just because he's been in Smash. He's another GBA rep and one clone is fine, so I think that's enough to keep him. The flame effects don't hurt him either, though I did kind of dismiss Hector's potential thunder effects so I won't really argue using this.
Chrom and Corrin I'm alright with giving the boot. Awakening was an important game for FE but Robin and Lucina is probably enough for it. I also did not really care much for Fates, but it was also a heavily pushed and successful game, so Corrin gets points for that as well as for being a transformation character, which is different. So I can see why they'd keep Corrin, but I'm also fine if they just use Robin/Lucina as the reps for the "3DS era" and skipped Fates. I'd also be open to Azura as a compromise with the "we need a lance user" fans and marketers; likewise, I'd be open to Tiki as another transformation character who helps to tie new and old FE together. You could also use someone like Sigurd in this spot as a legacy character who brings something interesting, namely his horse (assuming he'd be feasible).
TLDR:
If I picked the FE roster, it would likely be (in order of priority, Marth the first pick):
Marth
Ike
Robin
Lyn
Roy
Sigurd/Azura/Corrin/Tiki/Ephraim/Hector/Black Knight
Lucina (listed separately since she's an Echo)
The last slot with the slashes is admittedly an extremely difficult call. I tried to put them somewhat in order but some of them are pretty close. The top four are no-brainers for me, and I think Roy is alright if he's the only non-Echo clone. Leif, who was originally planned to be the Melee Marth clone, could also be used in place of Roy but there's really not much point in doing that unless you really want someone from Jugdral and you either don't deem Sigurd's mount to be feasible or want Azura/Corrin for Fates representation. If you could somehow find a way to make Micaiah or Celica work as a Robin clone then they could also replace Roy, but I don't view that as being especially easy to do.