passivity is expressed not in the finite verb but in the infinite verb subordinate to the finite verb. This happens in English (“it can be done”) as well as in French (“cela peut être fait”), German (“das kann getan werden”), or Swedish (“det kan göras”), to take only a few Indo-European languages as examples.
But on these expressions, “it/cela/das/det” is not impersonal–it’s a pronoun that refers to something specific that is doable. In the phrase under consideration, debet would be purely impersonal–there’s no referent for the impersonal subject. Isn’t that different from the English/French/German/Swedish phrases?
Here is the sentence from Cicero de Officiis 3.38:
satis enim nobis, si modo in philosophia aliquid profecimus, persuasum esse debet, si omnes deos hominesque celare possimus, nihil tamen avare, nihil iniuste, nihil libidinose, nihil incontinenter esse faciendum.
In this sentence, the subject of debet is the infinitive phrase si omnes deos hominesque celare possimus, nihil tamen avare, nihil iniuste, nihil libidinose, nihil incontinenter esse faciendum. Leaving aside the protasis of the conditional, the sentence can be translated literally “that . . . nothing greedy, nothing unjust . . . must be done [if we had the magic power to act with invisibility to gods and men] must be persuaded to us”, i.e., "we must be persuaded [by philosophical reasoning] that . . . "
In the sentence occupatis velocitate consuli debet, the infinitive phrase velocitate consuli doesn’t seem to me to be the subject of debet, but rather the object. Otherwise, there would be no complement to debet, and we would have something like “to be consulted speedily owes to busy people”. Owes what? “To be consulted speedily must”. Must what? The sentence from Cicero isn’t parallel.
I’m willing to accept that debet here is impersonal, but I still find it a little strange.