It's about 7% as of Kazuya. About 9% if you count Echo Fighters. Both are even less than an eighth, though they are still the third most populated series in terms of fighters by 2 (tying with The Legend of Zelda if we don't count Echo Fighters).
I'm pretty sure the biggest issue in terms of public perception is far and away how quickly they got here:
Roy gets recounted since he skipped a game, but even without that it's still pretty clear that Fire Emblem's roster kind of exploded during Super Smash Bros. for Nintendo 3Ds/Wii U and didn't
quite stop in Super Smash Bros. Ultimate. IIRC before Corrin, people were ragging about Pokémon for having only 5 (of course, nobody complained when Mewtwo was added because it's Mewtwo. lol). I also don't remember much complaint about Fire Emblem for this game until Byleth stirred up the hornet's nest, so I think it's fairly easy for it to blow over, it just takes a few years (which is admittedly longer than some would say is reasonable).