I'm very uncomfortable with a country begin able to make someone stateless.
I'm even more uncomfortable when it seems to be an attempt to get around that country's human rights legislation.
If the UK wants to allow its citizens to face the death penalty then it should come right out and say so - which may be a consequence of Brexit and being free of the ECHR (if Theresa May has her way). This feels like a mealy-mouthed way of abandoning national principles.
This. Very much this.
Making someone stateless goes against international treaties, in particular the ECHR (the convention). Extraditing someone to the USA (*) without assurances that the death penalty will not be sought, also goes against the ECHR. The Convention and the case law of the ECHR are very clear on that. This plan of the UK clearly flouts the legal principles it signed up to when it joined the CoE and signed the ECHR. If the UK carries this out, IMHO the only sensible response of the Council of Europe would be to immediately suspend the UK's membership of the CoE (with continued obligations with regards to the ECHR, of course).
Why doesn't the UK want to try them itself? After all, these are UK citizens who murdered, a.o., other UK citizens, so there are grounds enough for the UK itself to assert jurisdiction. They also murdered citizens from other western countries, so why not turn them over to, say, France or Canada (**)? The only reason I can see why the UK wants them extradited to the USA is that base blood lust prevails over the upholding of legal principles and the UK government hopes the USA will give them the death penalty.
Moreover, the USA is not a "world court" and should certainly not be treated as such - see also footnotes (*) and (***). If you want to do justice to the international aspect of their crimes, hand them over to the ICC in The Hague; that is a world court. While I agree, in theory, with the sentiment that Iraq or Syria should put them on trial, that is not practical: they have been captured now and should be put on trial now, whereas the chance that in the foreseeable future, there will be something like the rule of law in those countries is nil.
(*) or any other rogue state that has the death penalty.
(**) just examples, I haven't checked where their victims came from.
(***) Gitmo, extrajudicial rendition, torture, Gina Haspel.