The biggest difference between striking and grappling, is that it's easier to quit in grappling. If somebody gets you in a rough spot, you can give something up, let them take an arm or sink a choke and tap. With striking if you quit when your in a rough spot, you're going to get hurt or look like a pussy, like Rocky IV said "there's no easy way out".
Now do people actually quit in grappling matches when it gets tough, of course not. The fear of embarrassment is intensified, but in real life terms anybody that grapples at a good level is is going through similar amounts of pain and using similar toughness.
The "not wanting to risk head injury" thing is an excuse. CTE, pugilists dementia, etc, is caused by repeated unchecked mild concussions. Anybody that trains sensibly, in a controlled environment,with the aim being to not fight more than a dozen fights over a few years, would never come close. It's like saying that everyone that does BJJ will have a busted spine by the time they hit purple.