Well certainly the Roman and Italian Senators were not always eager to accept provincials as their peers, but the opposition to new blood was not as iron clad as it had been in the Republic. Most probably because many of the Italian Senators were themselves new men in a sense, having gained their positions with the extermination of many leading Roman families during the civil war. It was also precarious to argue against more provincials in government when a provincial managed to be elected imperator by the armies.
Yes, the Roman Empire was a function of the rich, but it was a function of the rich throughout the empire rather than solely at Rome. Roman law enshrined the property rights of the provincial notables, who were very much free to become Senators and Equestrians. The Empire was a contract between the imperial government and the local notables for mutual profit. The Republic was much more one sided in its imperial administration, outside of Italy at least.
And my point was that yes, while there was one man rule, the strong man in charge was assisted ably by many junior officers. The expanded Equestrian and Senatorial base resulting from the influx of rich provincials gave the emperors a pool of talent from which to gather imperial functionaries, e.g., Africans could serve as governors of Britain.
I agree there was an instability in the imperial system, mostly resulting from the procedures regarding the transfer of power from one Princeps to the next. However, when we look at the revolts and the civil wars, it seems like most of them were contesting a Princeps or candidate for Princeps with one of their own. The revolt was not against imperial rule itself, but who should lead it, showing the provincial elite had a stake in the imperial order. However, as you say the Crisis of the Third Century was a bit different.