Yep, I have the same fear. I especially didn't like the half ones because I was scared I'd fall into it and it would give way, open, and I'd fall out of the tub. Which I actually sort of did, in our last flat in Edinburgh. So it wasn't as irrational as I originally thought.
I also don't like how you're basically naked to the entire bathroom. Usually that's not a big deal but if you've got a frosted shower door or cloth shower curtain over a liner, at least someone could come in the bathroom while someone else is in the shower if need be. I guess you get the same thing with clear shower curtains, but even those usually have some sort of design on them so they're not totally see-through.
That being said, my parents just had a new shower put in their bathroom (in the US) and it's got a clear glass enclosure all around it. I love it!