Does all international travel include commerce? Every last import we have would have to come to a halt. No trucks crossing the border. No ships in the ports. Because they aren't automated. Shipments still need to be signed for in person, and those are points of contact. And then there are those in humanitarian aid and international healthcare who need to travel. And diplomats, politicians... Oh, and any person tasked with stopping others at the lesser border crossings, etc.
International travellers can spread it, sure. But there are still testing and quarantine restrictions when crossing the border that have been in place for the entirety of this pandemic. All it takes is one case to cascade into thousands, and it's damn near impossible to stop a single case, regardless of how draconian movement and travel restrictions are. North Korea would be the safest place on the planet as far as Covid-19 goes, were that the case.
Closing borders is security theatre. The only time it's ever going to be useful is when a virus isn't here to begin with; and Omicron was in at least 30 countries long before it was identified.
Addressing the unvaccinated/idiot-resistance and *properly* enforcing the rules we've already set in place would do far more than pretending stopping someone at the border is the holy grail of protecting us.