Alrighty... first off, let it be known that I am a rep grinder. I had 70-something reps at Exalted before Legion arrived. I have been grinding reps since the game began. The longest rep grind I documented was Wintersaber Trainers in 2005, which took me 238 hours of playtime to complete.
Now that the dust has settled on Legion, and all my zone questing is complete (except for the last few Suramar quest lines that are gated)... I am down to the only available way to gain reputation being world quests and random heroic queues. And I'm finding it to be VERY slow.
I spend a few hours each day fully clearing the map of world quests. Every single quest. Most award something like 75 reputation, and there seem to generally be 3-4 world quests per reputation type (except for Kirin Tor). In fact I can only think of one exception that rewards a significant amount of rep, and that's the Nightfallen training scenario. So the scenario notwithstanding, I'm pulling in maybe 300 rep per day, per faction (less on average for Kirin Tor since it rarely pops a quest for me).
I spent about 6 days getting to 110, as I had a busy personal life that week and I wanted to read everything as I went. Since then I've cleared the entire continent of world quests every single day. Kirin Tor has popped up one time for me as emissary, so I got one rep bonus item from that.
I've never seen any of the rep "insignias" drop from a chest. (In fact I have never gotten anything but gold or guild resources from emissary chests, so I think I'm just unlucky considering the number of people who are running around on fox mounts. ;P Also, someone else in my household who plays got a legendary from an emissary chest.)
I do a random heroic every day for the rewards and the 250 rep.
Anyway - let's assume I'm getting an average of 350 rep per day per faction, spending 2.5-3 hours per day to do that depending on what/where the quests are (some are fast to complete, some are slow due to poor design or spawn rate or bugs, or you waste 10 minutes trying to find it the first time you do it because so many of the map markers are wrong).
Doing the math, at 3 hours per day to clear the entire Broken Isles map and knock out a random heroic, 350 rep per faction times 6 factions = about 2100 rep gained per day. The amount of rep gain needed to get all six reps from Revered to Exalted, alone, is 21000 x 6 = 1,260,000 faction points.
1,260,000 faction points divided by the roughly 2100 rep I get each day clearing the map and running 1 heroic = 60 days to completely get everything to exalted. At 3 hours per day, that's 180 hours *just from Revered to Exalted*, and I don't have any faction at Revered yet, and probably won't until sometime next week.
Most of the questing got you to friendly or slightly into Honored, so you really are looking at at minimum 200 hours played time to get these factions leveled. Now, yes, it's better than old school Wintersaber in that it's six factions in 200+ hours, instead of a single one.
But don't let anyone tell you this is not a grind. It's a grind, just metered out in daily doses so you can't join a farm group for 8 hours at a time.