Westerners will say "but those relics are safer with us, since your country is fucked" without a hint of self awareness about who fucked up these countries to begin with. And regardless of the situation in those countries, it is THEIR decision where their relics get to be kept safe, not the decision of the people who stole it.
I'm not from the nation that stole it nor from the nation that created it but Iď love for the ancient artefacts to continue existing. I feel like they're not just a heritage of one nation, they're human heritage. The Taliban didn't create any of the artefacts they destroyed. They have no right to destroy such things just because they live at the same place as the creators. I'm sure the ancient creators would be furious if they new.
It's irrelevant at this point, for this topic. If leaving it means it'll be destroyed by whomever is in power at the moment, then leaving it is a bad idea until it's stabilized.
Countries can and do ask the museums currently caring for them to continue to do so if they're unable to provide adequate care for the artifacts themselves for whatever reason. Yemen and the Metropolitan Museum of Art came to an agreement over looted artifacts just a couple of weeks ago with Yemen maintaining ownership of the artifacts, but on display at the Met. It's still important for countries to maintain ownership of culturally significant artifacts that have been looted.