The quota idea is bad a priori.
None of the “refugees” will want to go to any of those states where the pickings are slimmer. They and their activist lawyers will sue to prevent them from being relocated within the EU, tying matters up in court for years (at the same time functionally disabling the court systems).
It’ll never work.
Australia was able to stem the flow of people on boats through its policy of diversion with few coming now.
But the policy has kept thousands on the islands in legal limbo for years because the Aussies are still giving their migrants the right to use their legal system to appeal for asylum.
The lawyers would definitely be involved if the EU did it, but such a policy might stop migrants from coming in the future.