Isn't the reason obvious?
The average modern game of mafia lasts 5ish days until one alignment has a sure-fire win. Limiting a jailor to 3 or more executions is pointless as he pretty much has infinite executions while it matters! (Bearing in mind he won't jail on lynch days and he's unlikely to always execute a target). How many games do you see with a 3 kill jailor where the jailor goes "Oh crap, soz guys out of executions."? Few.
And if two jailors survive to the mid game (and by mid game I mean 6 or 7 players left), it's almost always gg for the evils. I mean like, even if the evils are on par in terms of numbers with the town, they're still probably screwed by town killing scum faster at night than scum killing town at night! How fucking ridiculous!
Also, because of the strength of jailor, vigilante becomes simply weaker. Be honest, is there truly any situation where you'd say "Vigilante isn't even equal to jailor in this situation! Vigilante is simply better in this situation!"? There are very, very few situations where this would apply and even in those situations that's probably just because it's a cult save and the host did the right thing and heavily limited the jailor's executions. (So not worthy of a 1/3 chance when the chances are you want vigi 1/10th of the time)
Jailor is also much easier to confirm than it's town killing counterparts.
BUT THAT'D ALL CHANGE IF JAILOR WAS LIMITED TO 1 KILL!
He'd have a sane level of confirmability for a town killing, he'd be far more tactical with his last execution and would fear running out, he'd be par with vigilante, and, what's more, he wouldn't be so ridiculous in double jailor situations stopping scum kill while killing scum themselves! It'd be the best mafia christmas present EVER dark.revenant!
Plus, in a really weird way, this will get rid of failors in public games! If the jailor only has 1 execution he's far less likely to waste it on an afk doc he found n1, or even a crappy jester!
P.S. If you did do this however I'd think it'd only be right to remove him from town power, as he wouldn't be as auto-confirm any more.
P.S.S. You're probably feeling naturally opposed to this idea because this is a big change to mafia! You'll miss the happy days of whiping out the whole scum and stopping them kill anyone easily, single-handedly as jailor and getting praise from the town! "Good jailor!" they said, I bet! And you know what? That's ok! That's natural! But do you know what the solution is? Man the fuck up.