Re that point about the transformation...
Some of the earlier plans for a KX/StP terminal for international trains would have trashed a lot of the area. As it ended up, much of the inevitably destructive (re)building for the actual terminal facilities has thankfully been on brownfield land (ie the old disused railway lands) - though some people lost their homes in the process. Worse than the rail development itself, however, is the surrounding "regeneration" that has gone along with it. People who've lived and/or worked in the area for much of their lives, and long-existing local businesses, would disagree with the implication that the local transformation has been positive. The development plans themselves brought blight and dereliction onto the local area for decades; locals lost homes and jobs; plans which had been drawn up for (locally much needed) social housing, a school, open space, sports and other facilities for locals, etc etc (on the leftover railway lands) were thrown out and the land was given to "developers" to build high-end shops and "investment homes", corporate offices, etc. This affected not only the remaining parts of the old railway lands, but quite a bit of the surrounding area too. Sometimes, to outsiders, an area can seem run-down and unloved, when for the people actually there it is a functioning community - a community which needs better resources, not obliterating and replacing with something different which is out of reach of the displaced locals.
I speak as someone who didn't "travel through" the area in the '80s, but as someone who's worked there for much of my life and lived in the area for some of the time too.
The "hard border" is more to do with Schengen than EU membership or not, and the UK being in Schengen has never really been on the agenda. So surely - unless there were passport checks on trains again - the problem of needing border facilities at every station served by Eurostar is the same as it's always been.