These are mostly good points, but there's another reason that hasn't really been touched upon, which is many middle earth inhabitants' inherent distrust of Gandalf (Elves and Animals obviously excepted, along with a few others eg Aragorn).
Take, for example, Theoden's original reception of Gandalf in TTT:
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...truth to tell your welcome is doubtful here, Master Gandalf. You have ever been a herald of woe. Troubles follow you like crows, and ever the oftener the worse...Here you come again! And with evils worse than before, as might be expected. Why should I welcome you, Gandalf Stormcrow?
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Granted, Theoden is not in his right mind in this passage. But still evident is a sentiment of mistrust of Gandalf, because he is generally a harbinger of trouble. Of course, as readers, we know that Gandalf's appearances extinguish rather than kindle fires, but Theoden and the people of Rohan could be forgiven for mistaking this, and thinking that he is a dangerous troublemaker, as his few appearances tend to be closely followed by the possibility of death and nice long rambles to helm's deep etc etc.
A similar sentiment can be seen in the Shire, where, after Bilbo's disappearance,
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the blame was mostly laid on Gandalf.
"If only that dratted wizard will leave young Frodo alone, perhaps he'll settle down and grow some hobbit-sense," they said.
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Gandalf is similarly seen as a bad influence by the shirefolk in "The Hobbit", which, unfortunately, I do not have to hand.
My point is that, to many people in Middle-Earth, Gandalf is a mysterious figure who comes and goes as he pleases, usually accompanied by bad news or mysterious disappearances. Thus, though Denethor is further-seeing than hobbits and, arguably, than Theoden, it would not be a surprise if he dreaded Gandalf's appearances, and saw him as a thorn in his side.
This is not to challenge any of the above points, most of which seem very valid, rather it is another small reason why Denethor may have disliked Gandalf - he is bad news, and, given how secretive Gandalf is, a lot of his good work would have gone completely overlooked by the people he was actually helping.