As Olorin, Gandalf was able to do exactly that for the Elves (Sil - Valaquenta
-"they did not know whence came the fair visions or the promptings of wisdom
that he put into their hearts").
If Gandalf's mission had been to influence thoughts or put thoughts in the
minds of others, there would have been no need for him to become a wizard.
But, as an Istar, he was sent by the Valar, reduced in power, more because the
Valar feared causing fear among men or making a mess of the place, which
normally happens when they get directly involved. And if you think about this
quote from the Sil - Ainulindale,
"And some have said that the vision ceased ere the fulfilment of the
Dominion of Men and the fading of the Firstborn; wherefore, though the Music is
over all, the Valar have not seen as with sight the Later Ages or the ending of
the World",
none of the Valar and Maiar (including Sauron, Gandalf, Saruman, etc) could not
have been sure what was going to happen next...
It's important to remember, though, that if the Valar were to come to ME,
Sauron would not stand a chance...
I agree with your other
points...
"... in storm he delights, and laughs amid the roaring of the waves."