Should there actually be a another variant with significant immune escape properties due to the current number of new cases in China, some European countries at least will again resort to the only measures they know how to implement, which means, in that event: Lockdown, it is.
No, they didn't. They implemented precisely those authoritarian measures that seem to be working at first (like lockdowns) but are neither sustainable nor even effective for any prolonged period of time (> 2 weeks).
That said, impossible for west/rest to systemically lockdown post delta/omicron, R value too high. PRC travellers already out there, whatever variant is going to go global if borders remotely porous.
However, and very much absurdly, the same people and organisations opposing closing borders were those supporting prolonged and repeated lockdowns, which pretty much puts you in the same situation, just with no clearly defined perimeter to control.
Closing borders will just buy you additional time. That's it. Imposing lockdowns on the other hand in the end will achieve nothing.