Like, the previous king was a clown, true, but this regime hasn't exactly been a steward of the people's happiness has it
If you picked a random baker and put him in charge he'd do a better job
The King was authoritarian, but also a bohemian. The Roundheads were religious fanatics. They succeeded in overthrowing the Crown and executing the King, but they also turned out to be insufferably religious. After Cromwell died, the population re-invited the deposed monarch's son back, under some conditions. He met those conditions; his successor did not, but was promptly thrown out into exile, because he wasn't able to consolidate enough power anymore.
Unfortunately the Iranian population wasn't able to reconsider their choice after Khomeini's death (1989), because the government was much stronger and much more willing to kill. Also because of the Iraq-Iran war.