It's just blatant false advertising isn't it? The fact is, tickets are available for these services.
There will be lots of people who do a search, see all these "not available" notes, and choose to travel by some other route, probably much slower and possibly more expensive. If they were able to obtain an off peak single for the LNER trains then yes maybe they'd be crowded and they might have to stand. But the same could be the case on any alternatives. If you dont want to risk standing, you can find a train with reservations available.
Have there been any attempts to report LNER to trading standards or similar?
I questioned them once on Twitter; there was a lot of fluffing about before admitting that actually no, reservations aren't compulsory on that service. Then a comment that they would look into the wording on the website, which of course didn't happen, then they just stopped responding.