Also imagine VAR taking 5 minutes on each sin bin decision on top of what we have already
If they had a sin bin and somehow decided the way to implement it was "we will review every sin bin decision and then put the player in the bin" rather than "we will put players in the bin and then review the decision, inviting them to rejoin the game before their time in the bin is up if the binning was unjust" that would be insane.
In that specific situation you almost feel like the hypothetical orange card for a sin bin could work like so:
This way referees who worry about being blamed for "ruining the game" with an early double yellow might punish players/teams where they'd otherwise find any excuse to avoid the second yellow.
This really would allow for more inconsistent decisions but it would facilitate punishing behaviours that ought to be punished but which routinely go unpunished.
The rules ("Laws" I know) keep getting written to be more objective, but the pursuit of objectivity is foolish when a lot of the decisions are always going to be subjective. Increasing the level of subjective discretion could actually make refs feel empowered to make calls they're otherwise hesitant to make because everything is so binary and clashes with the human element. Or it might not, but the situation now definitely needs fixing somehow... all that can go wrong is a different wrong.