For the last strand "Why would you include the option to put non-FE music in the game", I was just thinking if someone would want custom music is all. However, this is a flawed idea, as it'll likely be very unlikely they can even do that.
Second, looking at this idea from a standpoint, it is impossible for them to make this without a huge budget and a huge time span. Not only that, but the games could take months to make as you've pointed out. There's a lot of factors to consider, making Fire emblem maker a unrealistic idea in the end. Just be happy we have customizable characters to an extent, I guess.