This thread, more than anything else, illustrates the problems with hard borders. No other international service in Western Europe would be subject to this kind of circus.
I absolutely agree. Looking at it objectively, it's crazy that the UK is the only western European country where you can't hop on a train without any red-tape and travel to cities in adjacent countries.
When the UK finally joins Schengen (however far off that might be) and security theatre for the channel tunnel is removed, the increase in train connectivity between UK and continental Europe will be dramatic (with equivalent reduction in level of air travel alongside it).
As you say, it would also end the chance of terminal renovation halting international train service for months. The trains would simply divert to another platform (or station) once red-tape wasn't an issue.