It wouldn't work. A team leading 1-0 in the 86th minute would simply use all their challenges in quick succession, slowing the game down, breaking up momentum for the team pushing for the goal and just make the whole thing farcical.
Not to mention the absurdity of the ref missing an obvious incident, the video ref seeing it and no action being taken because the team who was aggrieved by the incident has no challenges left. If VAR can still intervene in the scenario then it's just the current situation but pointless additional challenges and that would make no sense either.
So whether it's VAR is still used but managers can request additional challenges, or if the challenges are for VAR to relook at decisions they've already made in the game, or whether VAR can only intervene once there's a challenge from a team - then all three are utterly ridiculous in their own, special way.
It's like the 'sin bin' argument. People just randomly pluck things from other sports with no other logic than..."it works in southern league amateur archery..". without actually thinking about the impact it'll have on football. Arguably that's what got us here to begin with. Works in other sports, all we need to consider. VAR turned out a great success with that mindset.
Challenges would just produce a further layer of nonsense to ruin the spectacle of the game.
