Good riddance I say...
I'll use an example from my experience then to argue against AP fares for a minutes (I know this is supposed to be on walk-on but it will include walk-on nearer the end):
I travel to London quite often. Various reasons really, but mainly for a connecting bash to another one or a number crunching spree.
Now, AP fares do exist (after waiting for them for years, still are on the Marches). However, this are not the easiest things to get sometimes. Occasionally they simply don't exist on the trains you need. That's a fact of life, sometimes they sell out long before you can get them. Where does that leave me? I can be looking 12, 11, 10, even as little as 6 weeks in advance (which allows for NR to get off their rear ends and let the TOCs open reservations) for cheap fares. Even at 6 weeks (which I definately need now to arrange time-off et al) they can be unavailable. For the longest journeys I make (one of which will be Hereford - Linlithgow in June and back), if AP fares aren't available very often I have little options left.
Thankfully though, London isn't too far away from me (still a long way off really from Hereford, let alone the extra mileage to/from Kington), so a walk-on fare is still reasonably acceptable. At £33.65 for an Any Permitted Hereford - London Terminals fare, this isn't too bad really. Allows me to go via Newport as well, which allows for faster and better Valenta thrash. There is also a £27.05 Saver Return which is Route Evesham, which whilst cheaper by £6.60 had to be turned down on Friday as there was not a train that would get me there in time. On that same route a Cheap Day Return is also available, in the region of £22.50 (I'm not going to check the exact price), which is handy sometimes.
Point I'm trying to make (ambiguously perhaps) is that I was in the same boat as many, many people who could not get an advance-purchase fare (I might have been able to get an AP to London for the way there, £16 upwards I believe, but coming back was incredibly difficult to plan for, as I didn't want to set myself to a particular train if we were late back and I ended up missing it) and/or needed the flexibility to get their train(s).
AP fares work for a lot of people, but whilst they usually work for me (my last bash to London from Hereford by rail only had been an AP single, £10.50 and a bargain to boot at that with a pair of Valentas), this weekend was a case where they didn't. I believe I'd have had to fork out £16 for an AP back too, so I paid just £1.65 in that case for the flexibility. Sorry, but that just makes sense!
Another instance where walk-on triumphs is my sister's upcoming bash homeward-bound next weekend. Going from Doncaster to Birmingham, on the core VXC network. Cheapest AP fare on the train she had to get was around £16 I think (this is with a Y-P). A Standard Open Single is £19.15 with a Y-P. OK, so there's still a fair bit of difference in the fares and that difference could easily swing the balance in favour of AP in some cases. However, she wishes to have the flexibility as she is not sure if she can make that train off Doncaster. So she's got the SOS to ensure maximum flexibility.