If there really isn't enough space (which I highly doubt) then hold people on trains for queue management where necessary. It's hardly rocket science!
There isn't enough space, and I think that the idea of holding people in trains is unlikely to work or be popular. Worse than holding passengers on planes for the same reason, because at least a plane is high enough off the ground that people know they can't alight easily.
You might as well have made the same arguments about building the Channel Tunnel or HS1 in general. There is never a guarantee of anything, but presumably DB/Eurostar would have to pay for the facilities to be remodelled. Having paid, it would very much be in their interest to make use of their investment by running the trains.
It is not the same at all. Running long high capacity trains to the nearby capitals, for both travel to those capitals and connections to other, existing, train services is surer and less economically risky than trying to cater for relatively small, diffused, markets further away.
Yes, DB/Eurostar would have to pay for the facilities to be remodelled and it is indicative that they have chosen not to. We can only speculate as to why that may be, and I would guess that E* have extensively modelled the cost of the remodelling and change to their current system of outbasing Border Force staff and have come to the conclusion that the possibility of longer distance business (which would still require sterile areas of platforms, extra guards, more and better trained E* staff etc and no mixing of intra-Europe and Cross Channel passengers) simply does not make economic sense.
I'd have thought it was plainly obvious what the economic advantage was?
Not at all obvious to me. Clearly it is not obvious to the professionals at E* and DB either (otherwise they would have done it already). So perhaps some enlightenment?
However: The market has changed and there are loads of people nowadays happily sitting in a train for 5 hours, just not to Frankfurt

Just witness the success of Trenitalia‘s Paris - Lyon service.
Surely Paris-Lyon is shorter than 5 hours on a Trenitalia service? I would want to know how much of their success is new traffic to rail, rather than robbing passengers from SNCF trains first (and that the service is economically successful rather than just passenger numbers from low fares). Still got a bit of a way to go before using it as an example for other new services.
My memory is failing me, but I'm sure I got a passport check on the train in the early days of Eurostar. Did that actually happen, or did I dream that?
It was right at the beginning when far fewer trains ran, but that was in a different era, and too many issues put paid to it. It is too expensive on staff, not compatible with real time checking of databases and runs too much risk of those not correctly documented arriving on UK soil/concrete and disruption on trains. Just not going to happen anytime soon.