They even have a small place in Sesame Street.

Shocker has tons of subsidiaries.

Don't you mean Cobra-Shocker?

God.
And he is doing so while screaming randon monster names "Fangire!" "Greed!" "Phantom!"

Why would he come here anyways?

Not many monsters to fight in this world.

The Neo Heisei shows take place in the same universe, and going by Fourze the Heisei Riders do as well, add to that the footage shown at the start of the show of the Heisei 10... and continuity got royally screwed up.

Onore Decade...

Yeah.
But can you imagine how awesome would it be for W to appear in OOO or Fourze mentoring Wizard, it'd be amazing.

It's not and sometimes they speak english anyways. It really only matters if you like the Grongi, and I really only cared for Yusuke and his supporting cast.

Team-ups were way more common in the showa times apparently, with characters appearing in each other shows from time to time.

It was a post credits thing iirc.
Or a commercial? I know it wasn't a full episode.