Look, I hate to do this because I'm a big DC fan, but he has actually benefited from moving between weightclasses in his career. I won't write a long post, but let's look at the stages in his career.
He won the HW Tournament in Strikeforce. He beat Big Foot and Barnett. Good wins, but they were not the Top HWs in the world at that time. There's no argument there.
He then comes to the UFC and beats Mir and Big Country at HW. Again, good wins, but they definitely weren't the top heavyweights at the time.
Then announces his move to LHW and stirs up controversy with Jones. He still has never fought the top guy in his weightclass. He beats Patrick Cummins and Dan Henderson (Neither are no where near the top of the division), and earns a title shot.
Jones outclasses him in the title fight.
Cormier then goes on to beat Gustafsson and Rumble. GREAT wins. This is the only time he has ever beaten the top guys in either weightclass though?
Then he loses again to Jones. and makes his move to HW.
He knocks out Stipe, GREAT win. And beats Black Beast. GOOD win.
So at the end of the day, DC has only beaten 2 top guys at LHW (3, if you count Volkan). And 1 elite guy at HW (2, if you count Lewis.)
In both weightclasses, he was able to cut the line by generating hype from switching weightclasses.
He didn't have to go through a line of contenders at LHW like Jones did and is still doing. He never had to fight JDS, Cain, Overeem, Brock, Carwin at HW like everyone else did.