He removed two tribunes in the runup to his assassination (Gaius Marullus and Lucius Flavus) after they had a few citizens arrested for calling Caesar 'King' as he greeted them. He also had Publius Sestus removed, ostensibly on charges of inciting violence (but more motivated by opposition to his land redistribution), during one of his earlier consulships. I suppose you would argue all of this was justified, but my point is that no matter how you slice it, Tribunes of the Plebs were far more democratically accountable to the people and had far more electoral legitimacy than Caesar ever did (having been declared dictator for life by a thoroughly undemocratic institution, the Senate). Tribunes served for a year, and if the plebs actually disapproved of their conduct, they could have chosen someone else. The Plebeian Assembly's ability to elect their Tribunes was, after all, one of the few powers left to them after Sulla's reforms.
I guess a modern analogue would be a Supreme Court justice declaring they are working in the interests of the people, ruling that all corporations above a certain size must be dissolved, then removing from office members of Congress that try to impeach them. You might argue that they're acting in the interests of the people (in their own judgement), but it would be indisputably undemocratic nonetheless.
Edit: forgot to mention in my little analogy, of course, that the Supreme Court justice is also a four star general with the military at their beck and call.