It's a complicated issue, lots of reasons, I'll recap
We have a cultural war going on in the US between city people and country folks, it's divided between political lines. Everyone in the rural parts of the US know what I'm talking about. "City people" are basically shown the end of the driveway immediately or never even given the opportunity for an introduction.
Department of agriculture has very strict rules concerning toxins {lead} use around animal production facilities.
People work longer hours in the US, there's less free time for recreational shooting, when people are off work they tend to shoot centerfire guns.
Much less gun control in the US means people have real firearms instead of "bb guns", serious airgunners are far and few between compared to real firearm shooters.
Real guns cost about the same or less than airguns in the US at least the airguns that are accurate enough for pest control.
There's almost zero tolerance for rodents in any industrial facility of any kind let alone food production where monitored by the USDA, relatively safe pesticides have made that possible with professional pest control companies. I own a pest control company and can count the times on one hand where I've seen enough rats to shoot in 14yrs.
To get insurance to cover yourself while doing any pest control in the US requires a USDA pest control license, an individual can't just go take a test and buy one of those licenses, it requires a 2yr training program by a certified instructor and a series of tests and documented field training. The only viable way to do this is to go to work for a national company, one that's willing to do this for you and those are far and few between because it's expensive. If they will do it for you they'll make you sign a non-compete clause. It's certain that to do this you'll have work for national company and long enough to become a second level supervisor.
Been there, done that.