The Shah son doesn't have the local support his father had. Part of the diaspora like him enough, but the clans that brought him to power are way less aligned with the British ans US than they use to be.
On the other hand, exchanging an anti-US dictator for a US-aligned dictator is probably a lot better for the average citizen because your country won't be embargoed anymore, you just have to accept US oil companies on your territory.
It's tricky because the opposition don't have arms so it needs some of the guys who do to turn.
The US/Israel are being quite brutal though - killing all the regime leaders (as in youtube https://youtu.be/2TZF8_wwAUs?t=572)