Melee are better when the raid has to move. Much better.
When there is no movement, ranged have no advantage. Melee can do the same sustained dps.
Single target and AOE damage, and the ability to soak are spread across the classes. The best soakers are probably Monks and Rogues (melee).
On some fights there is multi-dotting, but on others there is cleave. It evens out in the end.
As always, melee are better at add control (stuns, interrupts, slows etc).
Melee mostly have better burst (although ranged can do fine as well).
There are very few mechanics where the melee are at a disadvantage. Thok is more or less than only fight I can think of in current tier (during kite phase only – although melee have a massive advantage during aoe phase).
There are a lot of fights where ranged have more work to do than melee (e.g. Sha, Galakras, Shamans, Malkorok, Spoils, Paragons, Garrosh).
In terms of raid utility, there is little overall difference. Some melee are just unique and have unique raid utility, just as ranged do. Locks have gateways and DKs have Gorefiends. There is raid utility everywhere.
TLDR: They are balanced in this tier. OP is just plain wrong (I play a Rogue).