Yes, under the emperors the Senate was a joke (as witnessed by Caligula's horse being made a Senator). And even the office of the Emperor was for sale to the Praetorian guard. There was no “balance of powers”, there was only the absolute power of the Emperor, and the power of the Praetorian Guard to determine who would be Emperor.
And under an imperial system you also get effeminate “artists” like Nero, and vain madmen like Caligula. Neither of these two would ever have been elected Consul, and would most certainly not have been reelected.
The funniest thing I find about Roman history is how much the term “Dictator” has become a pejorative. The original concept was quite benign, and far better than any King. The Dictator was elected, and had absolute power only for a year or until the crisis was past. Cincinnatus was the ideal dictator, and the inspiration for the American city that bears his name and an association of the founders that gathered under the banner of his name.
Caligula’s horse wasn’t made a Senator.
The Roman system was all about separation of powers, and that was rooted in the oligarchic nature of the “Republic”. The Senators weren’t elected, so they established or altered various other popular bodies to meet some expediency. The Emperor had dictator-for-life powers, but the Senate controlled legislation.
The Emperor Claudius revived the pre-imperial office of Censor in order to remove unfit Senators from office. That the office had lapsed indicates just how out of control the senatorial oligarchy had become. They were, in Voltaire’s phrase, an assembly of despots.
The Senate didn’t always appoint the Emperors, sometimes it merely put its imprimatur on a fait accompli, such as when crazy or otherwise ineffective Emperors were deposed / murdered, for example when the Praetorian Guard (which was established by the Senate) snuffed Caligula and the famous and probably false “found me hiding behind the curtain” selection of Claudius occurred. But the authority to appoint Emperors lay with the Senate.
Claudius was one of the more conscientious Emperors. If the Empire had figured out an orderly system of succession (for that matter, if the so-called Republic had), the great duration of it might have been even longer. Had the Empire — which began over a century before Julius Caesar was born — developed an elective system of government, it might still be around today.