Denethor vs. Aragorn

[Morthoron]

Eärnil II was elected king of Gondor because of his generalship, his control of the Gondorion army, his lineage, and, most importantly, the lack of a competitor with an army in the area. Arvedui could make counterclaims until he was blue in the face, but he was way up north in Arnor, powerless to stop Eärnil, and lacking any clout with the council.

The same can be said of Aragorn. If Denethor survived, there would be little he could do. Aragorn had control of the army, was victorious against Sauron, had a claim for the throne better than anyone in a millenium, and was highly respected by both Prince Imrahil and Faramir; whereas, Denethor, had he survived, could be charged with dereliction of duty and perhaps attempted murder and treason. From a cynical standpoint (and not at all in Aragorn's character), all that had to be done was to reveal that Aragorn was the great Thorongil returned, and Denethor would have been sent into retirement somewhere unpleasant, like in a hut overlooking a slag pit in the Morgul Vale.