You can be the most powerful puncher in the universe, but if you can't defend the takedown it doesn't equate to anything. Take it from someone with a background in Muay Thai, Judo, Boxing. I'm more of a boxing/kickboxing fan and I have been critical of mma's talent pool and marketing, but it's improving. But the only pure style that isn't kamikaze is a grappling base. As to who could and couldn't cross over it's all down to the individual. As has been the case with guys from all martial backgrounds. For a referance point go and look at how Holyfield controls Tyson in the clinch and negates a large part of his offence.
Little known fact, guys like Dempsey, Johnson and a lot of the oldschool guys were well versed in catch wrestling.