Re: EUCJ
In this context, it does seem reasonable. Although, given the scope of what's at stake, perhaps it's sensible for both sides to back off and agree to a more obviously neutral party (if there is such a thing - dig deep enough and there's nearly always at least one vested interest pulling strings).
I suspect there's also an element of distrust, or at least pretend distrust, of the EUCJ on behalf of the UK gov. Gotta play to the home crowd, as in Tory Eurosceptics. Plus it makes for a decent tabloid front page, rather than another splash of our gov and its mates' bungling COVID incompetence.
It's also perhaps nothing more than a negotiation tactic, something the UK can back down over in exchange for an EU concession.