Yes. But it's also possible to register some non-US passports for GE kiosk use too; however, that additional passport update needs to be done in the proper way prior to attempted GE kiosk use at the US port of entry if wanting it to work.

The way this works is for the UK passport user to travel to the US with an ESTA and then present themselves to CBP as a US citizen arriving without a currently valid US passport. We have routines to admit such US citizens into the US even when without a currently valid US passport, and the CBP will then do what it takes to admit a recognized US citizen to the US.

A US citizen can attempt to get an emergency travel passport on short-notice or a passport-substituting international travel document/letter from the USG, but the chances of that working on such short notice varies considerably more than just applying for an ESTA and doing as mentioned in the prior paragraph in this post.