Actually, if you did that, you would probably have French border personnel in St Pancras doing these checks immediately before the British controls. And then, you would probably centralize such controls there for all Cross-Channel services instead of carrying them out in Paris, Lille, Brussels etc... the most expensive thing would probably to build space for it at St Pancras
And more than for night trains, such a system would be useful for Eurostar, since they could serve a wider range of destinations if a border control outstation wouldn’t have to be established everywhere.
So checks by qualified station staff at each stop (which you need anyway for the security checks) and a segregated waiting area (which you also need for after the security checks anyway) and platform would be necessary.
However, no reason not to have intermediate stops to pick up passengers, provided they have these features as well.
It’s not that I don’t completely agree with you that this is generally so onerous that nobody would take the chance.
However, in very rare cases (less so for night trains - and there, obviously rolling stock is at least as much of a problem - more so e.g. for a E* Frankfurt - London) it could just work and it really is the UK insistence to have immigration officers outstationed (which is obviously much more expensive than „normal“ station staff) that makes a difference.
As for night trains, E* to Brussels and sleeper from there will be the only possible future, probably. Unfortunately there is no really good connecting station for trains towards Italy or Spain, which might actually be more attractive for UK travelers.