You can easily do all those things in Champions, it just costs a lot of points. Or in some cases, not even that many points. While it wouldn't be appropriate for most campaigns, you can do this:

World Domination: Major Transform 1 point, Reduced Endurance (0 END; +1/2), Persistent (+1/2), Indirect (+1/2), Based On EGO Combat Value (Mental Defense applies; +1), Area Of Effect (4" Radius; +1), Continuous (+1), Penetrating (x2; +1), MegaScale (1" = 10,000 km; +1 1/4), Invisible Power Effects, Hide effects of Power (Fully Invisible; +2) (49 Active Points)

This is a generally undetectable telepathic attack that will, within probably less than 15 minutes of turning it on, make everyone in the world who doesn't have doubly hardened mental defenses into your loyal followers. Or make a more subtle change, such as installing a telepathic "back door" you can use to bypass their defenses and make your normal telepathic stuff nearly automatic.

For reference, 49 points is below average by superheroic standards. A rocket launcher could easily cost more.