Iranian regime wasn't doing that well even when it wasn't actively bombed. And "rally around the flag" only goes so far in a country that has been killing protestors by the thousands.
I don't see this war ruining Iran's regime overnight as is. But if it comes up with a sustained effort to pressure Iran, or a ground operation to topple the regime directly, it well might.
Hardliners and the IRGC have significantly more power than before, and however few moderates that remain have much less political capital and are at much greater risk of being purged.
If Iran doesn't win significant concessions tayt the sucker-punch attacks will never be repeated again[1], they are guaranteed to sprint towards the minimum viable nuke.
1. Bibi will refuse, obviously, and Americas capacity to leash him is questionable.