Whether or not it was true, the story has a different point than "Caligula was insane." The point was to show Caligula intentionally disrepecting the Senate. Augustus had maintained all the official forms of the old power structure, even allowing Senators to compete for the now-pointless title of consul and only rarely holding it himself after the early years, to give them something to aspire to and still pretend that they still had relevance, but the power of the Senate went into eclipse under Tiberius. By the time Caligula's in power, saying that Caligula is putting Incitatus on the cursus honorum on track to be consul in a few years is saying to all the other Senators that the job of consul, the highest honor any of them could aspire to, was completely pointless, ceremonial, and powerless, such that even a horse could do it.

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The Roman Senate tended to accept the absolute power of Emperors as long as the Emperors didn't rub their faces in it: basically every one of the listed traditional "bad Emperors" are people who alienated the Senatorial class who wrote the histories by reminding them how powerless they were. Was Suetonius right that Caligula wanted to make Incitatus a consul? Who knows, but if he did, the logic of it as a calculated diss to the Senate makes worlds of sense and is no reason to consider him insane.

Many modern historians believe that later Romans found it "trendy" to rip on Caligula and other such disconnected autocrats. I am not aware of any evidence Caligula ever granted title to his horse, or seriously considered doing so. Nor am I aware of any legitimate sources that Caligula even genuinely threatened to do so.

I'd recommend "Mythbusting Ancient Rome" by Sushma Mallik to dispel the myths about the horse. It was a party joke by a depraved man, nothing more.