I'm not sure I see where the problem is.
If you're an ordinary raider, questing gets you close to heroics, drops in normals supplement it, you get a weapon from Proving Grounds if you didn't get one from inscription/Archaeology, etc., you burn JP to fill in the gaps, and a judicious JC trinket/alchemist stone/etc. gets you in. Heroic drops, Sha PuGs, LFR if you're lucky, maybe a piece of crafted gear - gets you in to raids. Once you're into the first tier of normal mode raids, drops bootstrap you to the next tier (ilvl is higher than the next tier's LFR, even) - and as the LP said, you can drop dungeons entirely and focus on dailies. By the time you've despaired of finally ever getting the drop you need to move up - revered with one faction at that point should certainly be possible. You only need to do 13 dailies per day to cap your coins for the week. At that rate, you are at worst revered with your favorite and working on a second by the end of a month (four lockouts). I don't see a four to six lockout gate being a heinous restriction for something that was intended to be a gap filler in the first place.
If you're seriously progression-minded - well, extraordinary measures is what you signed up for. That's why it's prestigious, because it means that you not only had the skill to close the deal but the commitment to do whatever it took to get to that point.