This position, that it doesn't matter, is just as dubious as the opposite, that a dictatorship can't stay in power given strong opposition from the population (cough, Syria, cough).
Absent a coup, popular discontent is often how dictatorships go out of power.
Hemingway
“How did you go bankrupt?"
Two ways. Gradually, then suddenly.”
We don't have that much data to look at *
, but we do have examples of regimes that look well-entrenched until they collapsed, surprising everyone.
Shah, Iran 1990
Abstract: When recalling U.S.-Iranian relations during the 1979 Iranian
Revolution, many sources blame the fall of the shah on the failure of U.S.
intelligence to accurately predict the crisis and keep Washington, DC,
policymakers informed. That argument, however, ignores the reality that a
reassessment of U.S. policy never occurred during that troubled time, even as
the quality of intelligence improved, since the James E. “Jimmy” Carter
administration did not believe the shah might be forced from power.
Bebe Doc, Haiti
Widespread discontent began manifesting further in March 1983, when Pope John Paul II visited Haiti. The pontiff declared that "things must change in Haiti"...
Ceauscescu Rumania, 1989
However, Ceaușescu had misjudged the crowd's mood. Roughly eight minutes into his speech, several people began jeering and booing, and others began chanting "Timișoara!"[62] .... Images of Ceaușescu's facial expression as the crowd began to boo and heckle him were among the most widely broadcast of the collapse of communism in Eastern Europe
Tunisia 2011
The Tunisian Revolution (also called the Jasmine Revolution and Tunisian Revolution of Dignity[8][9][10]) was an intensive 28-day campaign of civil resistance. It included a series of street demonstrations which took place in Tunisia, and led to the ousting of longtime president Zine El Abidine Ben Ali in January 2011.
Marcos, Philippines
The People Power Revolution, also known as the EDSA Revolution[a] or the February Revolution,[4][5][6][7] was a series of popular demonstrations in the Philippines, mostly in Metro Manila, from February 22 to 25, 1986.
In Tianamen, 1989, it was the CCP's great luck that the protests did not spread to a wider segment of the population.
*
Furthermore....
significant correlation
Doing stats attribution on one factor correctly relies on two things: a large enough sample and being able to flush out other variables.
Asking this, with our limited sample size of relevant states, in the past century (previously most of the world's people had limited expectations of benign government), and with a multitude of other variables present, seems, to my techy self, to be a conceit that tries to inject a veneer of "hard science" certainty into what is by nature not a "hard science". That cuts both ways: on this Q's premise, that it doesn't matter, and on the opposite, that popular sentiment will prevail.