Would such a variant be any good as an alternative to 960?

Chess rules as normal apply to this variant with the exception of the beginning of the game:

The game starts with a blank chessboard. Players take turns starting with white and placing 1 of their 16 pieces on the board.
-Players take turns dropping a piece like in crazyhouse/bughouse for the first 16 moves.
-Players may only place pieces on their 1/2 of the board (1st 4 ranks for white 2nd 4 ranks for black)
-Bishops must be placed on opposite colors
-No doubling of pawns, each file starts with a pawn in one of it's natural starting position or up 1 or 2.
-Place your pawns and pieces in any order you want, but the final piece to place is always the king.
-The first move is after black has placed his final piece
-Castling is NOT legal in this variant as kings and rooks are already considered moved when they are dropped
-Normal chess rules apply otherwise

thank you !

Sounds like a mix of Placement Chess and Screen Chess, I like the sound of it. I used to play Screen Chess over on BrainKing.com, though I kinda stopped a while ago; the obligation to log on at least every few days to make moves even at the longer correspondence time controls got to be a bit much for me. Screen Chess was definitely a big part of what got me hooked on chess in general when I had only just started playing, though.

Placement Chess seems kinda cool in theory, but the thinking required is a bit abstract for me. That being said, with Screen Chess while going in with your own setup that you know exactly what the idea behind is is nice; I do recognize the essential randomness of having no idea what your opponent's setup will be and vice versa makes it partially luck-of-the-draw, which isn't an element there should be any place for in a game of skill like chess.

Your idea sounds like a perfect middle-ground; you can design a setup that you know the exact idea behind reactively to the setup that your opponent is designing as you do. I think immediately placing a pawn up front 'n' center along c~f files for the first placement will still be a common choice, but it would certainly be interesting to see how the meta for this variation evolves. I'll offer a name for this variation you're proposing, assuming it's not already taken by a different notable variant; "Setup Chess".