With the context clues from the show, I don't think Alastor getting away from Vox's deal using wordplay is entirely "because Vox was obsessed with Alastor he didn't think things through".
We've seen two types of deals in Hazbin – "I do this for you, you do that for me" deal, and a soul contract
I'm putting Alastor's deal with Rosie as the formar – they shook hands, there's no signed contract, and the conditions are "I, Alastor, will do this thing for you, and you, Rosie, will make me the strongest sinner". There's a set timeline, the deal will be concluded once Alastor does that unknown to us thing for Rosie. The deal broke because Rosie couldn't keep her end of the bargain. What I'm saying is, it's a finate arrangement
Alastor made a deal with Vaggi, although we haven't seen anything to come of it yet, I doubt we will tbh
Then, Alastor makes a deal with Charlie – "I will tell you this thing, you'll do me a favor that won't hurt anyone at some undecided time" and that would be that
Then there's the deal Alastor makes with Vox. Put a pin on that for now
As per soul contracts:
We obviously have Angel and Valentino – Valentino can make Angel do anything/do anything to him in the premises of the filming studio, and in exchange Angel– *gets shot in the head before I can start rambling about my headcanons on the topic*– and we can assuming that it's an indefinite deal, unless Valentino breaks the conditions/doesn't deliver. You sell your soul for something, no returns.
Alastor owns Husk, and the deal most likely is something along the lines of "Husk can keep his Overlord powers, but he can't operate as an Overlord, and Alastor can do whatever he wants with him", again, indefinite deal with some conditions
What I'm saying is, we haven't seen anyone else being part of a no-soul-contract deal besides Alastor. Vaggi specifically warns Charlie about not making deals with Alastor. I don't think no-soul-contracts deals are common. Why would they? If you want to make a binding deal with someone more powerful than you, that other demon might as well take your soul for it, yk? Also, Charlie instantly assumed Alastor wanted her soul, so most likely a soul deal is more common than the "I do this for you, you do that for me" deal
Vox falling for the very obvious wordplay is, yes partially to Alastor proposing the deal, but also because no-soul-contract deals seem to be a thing around Alastor and Rosie, and if said deals are common, there's always a "we're both out of this deal once we both do our part" bit. There's a clear conclusion that might be reached tomorrow, or in a century, but there's an expiration date to it. It's an exchange rather than a sell
MY FOR REAL FOR REAL POINT – Alastor didn't set a condition where the deal would be concluded (NOT BROKEN), Vox who works with soul contracts on the daily but not smaller deals went with the force of habit that a deal, like a contract, is an indefinite thing unless some condition is broken/not fulfilled, AKA he was a dumbass not only because he's balls deep obsessed with Alastor, BUT ALSO BECAUSE HE'S A CEO WITH AN ENORMOUS EGO AND THOUGHT ALASTOR COULDN'T POSSIBLY FREE HIMSELF! SO HE'S EVEN DUMBER THAN YOU INITIALLY THINK!













