Regigigas should not be D rank, plain and simple. He has base 110/110/110 defenses, a normal typing, great for special walling, and can run a Sub + T-Wave set to generally cripple Pokemon on the opponents teams. He can stand head to head with basically every single special offensive threat on this list and can take a few neutral hits from the physical side too.
Regigigas is no slouch offensively either. He essentially has base 80 attack, not bad for a wall. After 5 turns of being in(not too hard with Regigigas's incredible subs and some parahax) Regigigas magically transforms from a major defensive threat to a major offensive threat. Return + EQ gives him pretty good coverage. 160 base attack is Uber level, and 100 speed in NU is not so bad, especially when many scarfers and naturally fast Pokemon are specially based. You should NEVER base your end game plan around a Regigigas sweep, but it can definitely help weaken up and cripple the opponents team, and will sometimes end the game right then and there.
A major problem with Regigigas is that he can not touch Haunter or Misdreavus, and this gives Haunter a chance to set up a sub. You never want to give Haunter a free sub. This really brings Regigigas down. And a good Pursuit user is highly recommended if you are going to use him. You could use Zen Headbutt as well, but then Steel types and Rock types give you problems.
No Pokemon can quite do what Regigigas does, but Lickilicky is very similar to Regigigas, in terms of stats and typing, and Lickilicky has Wish and Swords Dance, Regigigas without Slow Start is a much larger threat than Lickilicky with Swords Dance though. So really the only reason to use Lickilicky is if you want Wish and Dragon Tail. Instead of Thunder Wave, better defenses, and the ability to do some major damage.
Because his capabilities of defensive and offensive power. I would recommend moving him up to C tier, possibly even the B tier, if Lickilicky managed to be an A tier wall.