I don't think this is possible. I've seen many raiding teams who dedicated time slots of no more than two hours to a raid night and with the growing popularity of Openraid and raid scheduling for flex modes that take between 45 minutes to 2 hours typically I no longer think claiming time is the restriction works. In a truly worst case where you NEVER have more than one hour at a time to play, even LFRs are unfeasible because of the tremendous frequency of wiping due to rampant failure. In this case, I couldn't, in good conscience, recommend playing WoW at all.
Many "Casual" LFR players dedicate many hours a week to clearing LFR, though it may be spread over the course of several days, this investment of time still means that pursuing higher levels of raiding is possible. Flex modes are a tremendous improvement to LFR, they fully encourage cooperation and communication between players and benefit from players establishing lasting contacts and familiar teams. I have no problem believing that in a few months a team of ten strangers across different realms could meet and form an effective "Guild" raiding for a single hour on four different days to clear all of Flex modes on a weekly basis.
But I'm not advocating the destruction of LFR, although I do believe it still needs tuning and design fixes. It has tremendous power as a tool to show people the encounters in a low risk environment. I just feel that the player base as a whole is fully capable of reaching at least Flex level raiding even at the minimal casual levels because of the myriad of cooperation tools available to them.
Endgame content should also more heavily favor 5 man dungeons, the distinction between normal and heroic dungeons that was a critical point of Burning Crusade is something that should return, though perhaps in not such an extreme degree. The bottom line is that Heroic should feel heroic, as it stands not many things in WoW really do that well besides the upper level bosses in SoO normal and of course Hard modes themselves.