Earlier quoted context omitted.
Yes it's a bit more expensive but the trains themselves are way more confortable, most of the time on schedule and drive at full operational speed all the time because they rails are made for it. With TGV on the other hand you have a few sections which are standard rails and thus you the train drive at a normal (low) speed...
More comfortable than the TGV? The train I'm most familiar with is the Thalys, the high-speed train from Amsterdam to Paris, and I'm not sure if it's more comfortable than other TGVs, but it's always a joy to travel in. I recently went to London in the Eurostar, and they'd managed to make the train experience feel like a plane. Very disappointing.
Regarding the Eurostar, it works like that because the UK is not in Schengen. As such, border control needs to happen. Not to mention the potential issues with terrorism. And the Eurostar is net inferior to any of the Shinkansen trains.