If the AMOC is strong, then closing the strait would cause less fresh water to flow out of the Arctic Ocean and into the Atlantic, they found. That would help keep the North Atlantic salty and the AMOC stable. But if the AMOC is already near collapse, then closing the strait would have the opposite effect, destabilizing the AMOC further. The timing, in other words, is key.

https://archive.ph/Vd86e

We’ll try anything but not burning oil.

Russia is investing VERY heavily in there Northern Sea Route accross the artic, and would need to be compensated. China and all other nations would have to agree to closing an internationonal water way. And then there is the distinct possibility that durring the very long construction process, narowing the strait will accelerate ice loss, possibly catestrophicaly, and engineering challenges or financial difficulties, or war could strand it that way.Nasty.

Edit: wiki desribes earlier plans to dam the strait, https://en.wikipedia.org/wiki/Bering_strait