Allot missunderstanding and too much "Caligula the Movie" discussion here
The Classical Story as Caligula as "De Sade of Rome" came from Roman Historians who lived generations after Caligula was murder
and only two document survived by
Philo and
Seneca, first made overview of early reign of Caligula, while Seneca just collect anecdotes on Caligula's life.
The Rest were written 80 and 120 years after Death of Caligula and full of Gossip, legends, anecdotes and Propaganda !
The Current ruling Emperors wanted to be in better light as there illustrious predecessors
Today Historians made allot of Efforts to see the true Story behind the handed down Gossip, legends and anecdotes.
it seem Caligula try to reform the Empire, but failed against Senat and faced rebellion in Army.
the Horse as senator was just a insult of Caligula, toward the opposite senate
the Tale of his Army attacking the Sea, was his punishment as the Troops refuse to Invade England and Irland.
Also is some true behind the story Caligula plans to Move the Empire capital to Alexandra (today Egypt).
also allo exaggeration about Murder and Rape under Caligula reign, it was typical for Roman politician to murder there opponent or use Rape to humiliation there enemies.
if now Roman Senators or Emperors Cesar, Augustus, Tiberius, Caligula, Claudius, Nero. All of them use Murder/Rape as tool for there politics.
So was he Killed because of his hell-raiser life style ?
The Reality is more common, he made several purges in Senat, Army and his the Praetorian Guard.
instead to prevent conspiracy, it United then what let to successful murder of Caligula
Oh hell were those plotter surprised as modest uncle Claudius became emperor...