We're not held hostage by any international law or treaty. Fact.

Held hostage? No. But we are still constrained by them, in the sense that we cannot violate them without consequences.

Those consequences aren't analogous to what happens to individual people if they violate the laws of their countries. There's no uber global-government that can put the U.S. in "country jail" for breaking international law, the way you can be arrested and imprisoned for breaking national laws.

But if we break our international commitments, then we lose some of our ability to get other countries to honor their international commitments. That's the currency of international law. You don't throw other countries' ambassadors in prison so that they won't throw your ambassadors in prison, and everyone benefits if ambassadors can do their jobs. The U.S. (like most countries) benefits from a massive amount of international law that protects our interests abroad, everything from mutually honoring copyright and patent and other IP regulations (so Apple can sell Iphones in Europe without them being knocked off) to mail treaties and air travel treaties and a ton of other ones.

Human rights treaties are especially important. Partially because they allow our own citizens to travel abroad in relative (not 100%!) safety from the depredations of foreign governments, but also because international human rights law has traditionally been one of our more potent weapons against the sphere of influence of dictatorships like China. We're different from the Chinese (we argue) because we honor human rights and they don't, which makes it easier for us to try to arrange coalitions and alliances to check their power.

No one can stop us from breaking international law, but the consequences to U.S. interests are much, much higher when we do things that violate our treaty obligations than when we do things that we've never promised not to do.

Obligations under international law with respect to asylees are pretty minimal. All we're required to do is give them a hearing, and not send them back to their home countries if they will be subject to persecution. You can expel them if they don't meet the standard, and you don't have to let them loose even if they do. You can detain them in refugee camps for the rest of their lives, if you choose. So given the almost nonexistent benefits of not providing the hearing, it's absolutely not worth the cost of breaking international law to suspend asylum on a permanent basis.

And, as has been mentioned a few times, the President doesn't have the power to do that on his own anyway. Absent an act of Congress to amend the statute to abrogate the 1959 Convention, the President is required to allow the asylees to remain in the U.S. until they get a hearing on their claims. It's not a "Magical Protection Shield" - it's a U.S. statute, and both Trump and Biden have been enjoined from violating it by the courts in each of their respective Administrations. The Executive simply does not have the legal authority to return asylees to their home countries without providing them a hearing.