I'll answer te last question first. I find that simple loop lanyards on larger knives help me comtrol the blade better if I tie the lanyard just right. So yes, they really do help, at least with me anyway. On smaller and medium sized knives I don't really need them as I have better blade control, but I make sure that every one of my knives have them.

With some of the fancier lanyears you can get a surprising amount of 550 cordage into a surprisingly small lanyard. That couple of extra feet can be used to make a firebow, spare shoe lace, sling, lashings, etc....

I've never had a lanyard keep the blade from slipping out of my hand. However, I only really use the lanyard on bigger blades anyway. And I've never had one hand up on brush, that's notto say it doesn't happen to people, just not me.