Both these are spot on. Where express buses/coaches succeed is where they can minimise the point to point time difference. That's usually the actual distance isn't that far and is usually helped by non centrally located rail stations. For this, see Bristol to Bath, York to Leeds or Swansea to Cardiff. Also, because of the distance, the price differential isn't generally so great in actual terms (rather than as a percentage).
For long distance travel, the time differential is magnified but so is the price differential so for those on a budget, it explains with NX or Megabus still works. Note that in the last 20 years, the rail companies have been more aggressive in pricing in filling up empty seats so there are noticeably fewer coach routes as even the price difference has narrowed.
You can add plenty of examples where an invigorated rail has killed off or seriously depleted bus/coach services viz Bathgate to Edinburgh, Southend to London, Galashiels to Edinburgh.
The removal of bridge tolls saw road traffic across the bridges increase by 10% in the first few months; how many of people who used to do an unofficial park and ride in Chepstow or Magor and save the toll now just continue their drive.... It's a service whose lifecycle may just have come to an end.