This idea kind of came to me the other day while I was grinding Valor, but what if there were an additional difficulty for 5-mans that are geared for players that have JUST hit the level cap?
Think of it this way. You have your normal 5-mans while you level. Once you hit 95 (or whatever the new level cap is), you'll be able to queue for Level 95 dungeons. These instances are identical to normals, but the numbers are adjusted for capped players, and all loot has a higher item level. Players who only intend to run LFR will be fine with stopping here and moving on to those. Players who want to gear up further for Flex or normals will move on to heroics.
Unlike current heroics, these new age heroics are quite a bit more difficult, and not just as far as DPS and healing requirements. Bosses could have new mechanics exclusive to this difficulty, as well as drop new loot. In fact, heroics could have entirely unique encounters that normal modes and Level 95 dungeons don't have. Basically, the encounters have more of a raid-like quality to them, sort of like practice for when they move on to proper raiding.
Challenge modes utilize the same template as heroics, but like now, your gear is scaled back to, say, somewhere in between normal mode gear and Level 95 gear. Bosses drop loot, but only if you meet certain criteria, e.g. killing the boss within X amount of minutes, or performing some kind of action, similarly to the Glory of achievements.
IMO, this would provide new avenues of gearing, depending on how you intend to play at cap. If you're interested in LFR, you can stop once you've gotten Level 95 gear, and proceed to gear up through LFR. If you're not too keen on LFR, you can move on to heroics, and from there take on raiding. Challenge modes are for those crazy few who are gluttons for punishment and will do anything for achievements and fancy mog sets.