Sounds like both forums (striking and grappling) intuitively know there is more that is needed to counter chaotic everyday defensive situations than just their own condensed art, realistically. Especially this scenario where someone is grabbing you by the collar to punch you. That specific situation is a blend of both grappling and striking, so it requires familiarity with both to be able to counter it.
That's not to say you can't or shouldn't have a specialty that you are best at. It seems to work best in MMA if people have a specialty (striking, esp. boxing as of late
) and supplement around that.
When Jack Dempsey was asked by the government to teach the U.S. troops how to fight, he also felt the same way, that a healthy dose of some grappling be instituted into the training necessarily.
Boxers used to wrestle as well as box because the two work so incredibly great together. I'm actually glad that boxing further refined itself into almost pure striking so it could further evolve in mechanical efficiency. It's not like they STOP you or discourage a boxer from separately training wrestling. That's probably the most effective way to train more than one high level art-- separately, from what I've seen anyway (for most people).