Every adcom/attending/etc says that unless a school specifically says they're receptive to LOIs then they really just don't care at all. Who knows if they even read them lol. I dont personally think
@Star224's theory is reasonable though, I think if they really want you then they would just accept you. If you haven't been accepted they're probably just a little on the fence about you still and want to see how the rest of their class shakes out first.
(btw I interviewed in early fall, also sent an LOI without response, no acceptance yet either sigh)