It's a cool concept but the first naive thought that comes to mind for me is that white could just easily dominate by taking advantage of the fact that taking a queen is almost always the top engine move. So just by maintaining relative king safety on white's side, you just open your queen early and make sure that every move there onwards hangs your queen in some fashion. It's very easy to hang a queen. You just have…
Second, if you ever hang your queen two ways at once - one of them could be a less optimal take (-5 is not as good as -8)
Third, whoever is a move ahead in a race of taking pieces will be the first to run out of weak pieces to take. Their available move pool is shrinking faster. Not sure how it would play out, black would need to cater to it by removing defenders and hanging pieces of their own, etc.
That said, first move advantage does seem strong still due to how forcing a queen can be. An example would be 1.e4..e5 2.Qh5..d5 3.Qxf7#