Let It Go should've been at the end
It's about Elsa embracing her powers. That doesn't happen until the end.
shareIt's also about her moving past the shackles of society, but also a little bit about her ignoring the demands of love and community.
Because her character - and the larger plot - is going through such a dramatic shift at that point in the film, some kind of song was necessary and Let It Go fits the bill.
A reprise at the end might have been cool, though...