This variant sounds interesting at first, but there is one key flaw. You are using the assumption that there really is an interesting pick and counter pick strategy. I believe this is not the case. In a nutshell, white should pick the most valuable piece available. Then when black gets to counterpick, but there aren't really any "good" and "bad" matchups, but rather just pieces with different values to choose from. He should also pick the most valuable piece.
In practice the players might not always choose the most valuable piece because they want to have fun or don't know which piece is best, but they will put themselves at a disadvantage from the start.
Also, no matter what you do, it is impossible to remove the first move advantage. You can compensate it, but not remove it.
Yesterday I was checking out S-Chess on YT introduced by Yasser. As I was listening the explanation (check out https://en.wikipedia.org/wiki/Seirawan_chess to understand if you don't know). I thought, "this changes the rules a lot". Spawning a piece after playing seems too unnatural for chess.
After thinking more, I thought, couldn't it just be a game where in the beginning the players choose what piece they would like as their "queen". Basically the king chooses what ally he should bring to battle. So you could only start with the "Queen", "Marshall", or "Chancellor" (or "Hawk" and "Elephant" as Yasser names them).
White would be the first to choose, since they also play first. This would also remove the advantage white has of being the first one to play (black can counterpick).
Let me know what you guys think. I had to post this since this was bugging my mind for some reason.