I can't agree on this one. Giving a villain reasons independent of the hero makes them less generic and more well-designed in my mind.
To be sure, there are villains that absolutely are - and should remain - tethered to their hero. Key motives behind everything Luthor, The Joker, Sinestro, and Professor Zoom do should include inflicting maximum humiliation and/or misery on (respectively) Superman, Batman, Green Lantern and The Flash.
However, there's no reason a Gorilla Grodd, or a Vandal Savage can't view themselves as beyond such feuds and launch schemes that aren't necessarily intended to include throwing down with a particular Spandexer. In fact, you'd expect a simple smash-and-grabber like Mirror Master or The Tattoo Man to go after schemes that let them avoid their usual hero. In a similar manner, you'd expect a mercenary like Deathstroke or Chesire to go where the money is, rather than continually seek paydays in a particular character's backyard.
I always though Ultra-Humanite an ideal adversary for Mister Terrific.