But US phones are mostly frequency locked to carriers.
Kinda sorta used to be more but not so much now.
Part of the confusion comes from the fact that, unlike pretty much the rest of the world, US carriers did not standardize on the GSM technology family. Back in the day, AT&T and T-Mobile chose GSM, while Verizon and Sprint chose the CDMA technology family. So right there you had incompatible technologies between carriers that didn't exist most anywhere else in the world (except for Japan and Korea, mainly).
Phones built to run on the GSM family of technologies use SIM cards and are generally "SIM-swappable." Some phones, typically the ones bought on a contract for a discount, are "SIM-locked" to a carrier meaning that the phone has to be unlocked by the original carrier before the phone can be used with a SIM from another carrier. However, pretty much all cheap/prepaid phones are not SIM locked and can be swapped easily. Phones built to run on CDMA family of technologies do not use SIM cards so are a moot point for "SIM swapping."
Oh, and don't forget this in your research - there are at least three popular SIM card sizes roaming (no pun intended) in the wild these days, and they are mutually incompatible. So don't expect to take the full-sized SIM out of your feature phone and transfer it to the micro SIM slot of a Galaxy S4 or the nano SIM slot of an iPhone 5s ... although of course you can buy adapters that will make smaller SIMs fit into larger slots.
In case you're wondering, the fact that all four major US carriers are using LTE nowadays should make the situation less complicated, but it really doesn't. That's because there are virtually no phones out there that use LTE exclusively. Unless your carrier has VoLTE deployed, your "LTE" phone is just using LTE for data but is falling back to 3G CDMA or GSM/HSPA to make your voice calls. So even though every LTE phone has a SIM, phones on legacy CDMA carriers aren't full "SIM-swappable."
Long story short - SIM swappability these days is far less about carrier locking and more about SIM sizes and which network you're trying to use. Good luck!