You seem to have missed the point.

It’s not the traceability of the phone. It’s the contents of the phone.

The contents of our phones is deeply personal and some courts have ruled that makes them part of the fourth amendment protections, but it’s not made it to the Supreme Court (afaik, ianal) and border patrol doesn’t care as this case makes evident.

The benefit of a burner phone is that you don’t knock out your primary phone in order to remove “incriminating” evidence like that time your friend texted you that Donald Trump is an orange bellend.

Its possible to own a phone and never use a SIM. This is the recommend option. Never connect to a cell tower. Just use WiFi.