As it happens, last night, I looked at prices from York to London for early on Thursday morning. There are no Advance tickets at all on any train prior to the 08:13, meaning every train is priced at £172.50 single. This is matched northbound at tea time.
Whilst York isn't part of the "trial", if anyone has any doubts as to where it will ultimately lead - this is your answer. This will become the "standard fare" at any busy time, "peak" or "off peak", where Advance tickets, which includes 70 minute flex tickets, simply won't be available.
I don't think there's much evidence of this. Even during the Fringe you only really saw the Anytime pop up on traditionally off peak trains where it was the last couple of seats and they really wanted to push people onto other quieter ones. There has been a fare increase (roughly 20% for on the day purchases in my observation, suggesting that they think Newcastle* was priced about right but Edinburgh worth a fair bit more than an extra tenner) but not a simple "Anytime for everything" approach - they could do that but they haven't.
The only other time you see it is where it's a connectional XC+TPE/LNER service (involving the York semifast, usually) and the quotas don't line up, though given that almost everyone buys on Trainline these days and that does splits I doubt anyone is paying that on those trains.
What I do think they might call for next, though, is either the abolition of the Anytime or the ability to increase it well above its present level. £200 for London-Edinburgh on a fully flexible ticket valid at peak time is borderline reasonable and would be comparable on distance to a London-Manchester Anytime Return of about £200, which coincidentally is about what I think that fare should actually be rather than the near twice that that it is. If you compare it to London-Manchester and consider that that nearly £400 Anytime is priced about right, they might see Edinburgh as being viable to near double if you look at the distances.
One thing that will be very interesting is what the pricing on 24th Dec is like when looked at on 23rd...
* Newcastle and Edinburgh walk up fares are and were about the same, so either one is overpriced or one is underpriced...