As long as you're just traveling with one company it's usually fine - especially DB, you can usually just hop on the next train.
However with a journey spanning multiple companies you're out of luck... and with seat reservations on TGVs you commonly have to wait until the next day.
It's something that shouldn't be too hard to fix: Give passengers an easy and forgiving way to continue their journey (and make the causing company pay) - ideally this should automatically show up on the App and give the passenger options of new connections etc.
None of this fixes seat reservations on TGVs though, which are also annoying for offers like Interrail/Eurail... EU should probably start regulating seat reservations /s