Long-term rentals indicate tenants that are stable enough to at least afford the lease. They are subject to at least some vetting (including background checks) prior to moving in. Short term tenants can be anyone. No background checks are conducted.
Strangers, even unvetted ones, almost never pose a danger to children. The vast majority of harm done to children is done by friends and family. Having more strangers around makes your kids safer, if anything.
The danger comes from the self selected, if you have a crowd of random people and you choose one at random, then the chances that they have malicious intent are related to the incidence of that in the population; OTOH if you ask for volunteers, or worse, if someone spontaneously volunteers then the chance is way higher...
If strangers were afforded equal access to your children, the numbers would not be so favorable. Having strangers around does not make your kids safer. At best, your kinds would be just as safe around strangers. At worst, they would be exposed to far more risk.
I hear this a lot and my guess is this is simply a function of how much time family and friends spend with a child (in relative privacy) compared to complete strangers. The surface area of attack is way smaller for random people; they don't have the "reasonable" opportunity.
I personally feel that short term rentals work very well in some places, but they can be very disruptive to neighborhoods as well. I guess it comes down to whether you feel that the preservation of the residential nature of a neighborhood is a legitimate reason to regulate. As you can probably tell from the way I set this up, I do.