That is pretty much what TCP does, except that it doesn't "request" missing packets: the client just acknowledges the ID of the last packet it was happy with.

That is pretty much what TCP does, except that it doesn't "request" missing packets: the client just acknowledges the ID of the last packet it was happy with. It requires a sequence though, so that you know that the client can know that packet it just received isn't the one it expected, but you could build that with a chain of IDs like you're proposing.