Nintendo themselves stated that in Japan at least, female players are the MAJORITY of the Fire Emblem fanbase. You can see this belief in some of the Japanese commercials seemingly marketing to women. (Mystery, Blazing Sword, and Sacred Stones in particular.)
.....Which makes their whole move towards pandering to unsavory male audiences as of Awakening all the more questionable. Why are characters like Tharja, Camilla, Nowi, Elise, etc. now at the forefront when the company themselves believe more females are playing the games?
I mean, I know the real reason. (Waifus make more money than husbandos.) But still.....
As for whether or not a female protagonist would make the game better..... lolno. Especially not with modern IS. We really can't trust IS to competently write female characters. If you took away wanting to f*** Daddy from Lucina, she'd basically have no personality beyond shounen anime hero quips. If you took away wanting to f*** Corrin from Camilla, she'd be a complete blank slate. Even their rewriting of Celica to make her naive complete with a scenario that wasn't even in the original game (Jedah didn't trick Celica, he just trapped her party in Duma's cave and Alm had to come to their rescue.) is still not quite as naive as Eirika was. And then along came Corrin.....
I may not agree with what you have to say, but I will fight to the death for my right to fight you to the death. -Stephen Colbert