Caesar not only ran, he was elected consul in 59.
It was a crooked election, but then they all were by that time, and it was crooked on all sides.
The best description I've heard of the later Roman Republic is that the government had been captured by a mafia of aristocrats. They ran the government in their own interests and used State resources to fight their own private wars. The system was utterly unsustainable and WAS going to collapse.
The only real question about Caesar is whether he was out to gain ultimate power for his own aggrandizement or because he saw that a monarchy was, given what was possible at the time, the only way to "save" Rome. Or possibly a combination. He was killed before he could really tip his hand one way or the other.
That the Republic was utterly unsustainable can be seen by the way no serious attempt to return to it was made after Augustus took power. It had totally discredited itself, much as communism totally discredited itself in Russia. Nobody believed in it any longer, so it fell apart.
I am not at all persuaded that Julius had any intention of "saving" what was left of the Republic, but that notion in any case became moot upon his death and the ascension of Octavius and his cronies.
Armstrong's piece lost its credibility with me initially with his characterisation of Cicero as a "flake". Talk about rewriting history, good grief!