This is an example of the sort of simplification that we’re constantly told passengers want.
Except that an Advance ticket was always an Advance ticket, no matter what the price is. Lining up all of the prices simplifies nothing from the passenger perspective. The conditions continue to be "booked train only".
Simplification would be streamlining the walk-up fares, such that a flexible ticket from A-B is a flexible ticket from A-B. No TOC-specific restrictions, and if any peak restrictions need to exist then they should be consistent with similar journeys.
To take Manchester to Manchester Airport for example, there are three sets of TOC-specific restrictions, with different definitions of "peak", plus Northern offering Advance fares for very short journeys. All for a 15 minute stretch with a high proportion of foreign travellers and inexperienced rail users. Then factor in the tiniest bit of late-running and "isn't this the 9:59?", "no, it's the late-running 9:55 and your ticket isn't valid" becomes a circus.
On another route, someone asking for a return ticket turns into a Mastermind quiz:
"What time will you be returning? If you use one of our services peak hours are x-y and they depart at z past every other hour. However for two quid more you can have a flexible ticket and there aren't any afternoon peak restrictions on that..."
Again for a 15 minute journey.