> They want to use the same identification techniques at entry and exit and match them.

The US doesn't even try to have general exit controls, though, and the routes of egress that DHS has the kind of presence at to implement facial recognition ar already have supposedly positive identification procedures for what is theoretically more critical and immediate security purposes in place, making facial recognition at those locations a very low value in improving ability to narrow down potential visa overstays.

Which isn't to say this isn't the reason, just that it's a very poor reason.