Why do all shower cubicles have open tops, and does it have to be this way?

I have a small bathroom with a traditional 2 sided shower cubicle in one corner. Like all shower cubicles it has an open top. The bathroom has both an opening window and a working extractor fan.

If the first person to use the bathroom in the morning takes a shower, then bathroom quickly fills with steam and condensation forms on the walls (even with window open and extractor on). Anyone else who then uses the bathroom in the next half hour or so has to put up with a rather damp and unpleasant environment. (situation is probably exacerbated by location, I'm in northern Europe, the showers are hot, and the bathroom is cool – ideal conditions for condensation)

The extractor fan is in the bathroom ceiling above the shower cubicle, I can't help but think that if the cubicle was sealed (i.e. the walls went all the way up to the ceiling) then steam from the shower wouldn't get into the bathroom and the extractor fan would suck it all out before it had the chance to spread into the rest of the bathroom and condense on the walls/windows/floor.

Or am I missing something? Is there a good reason the walls of shower cubicles never reach the ceiling?

UPDATE – thanks for the suggestions about alternative ways of reducing condensation, but that's not really the focus of the question. Is there a good reason for shower cubicles being open at the top? The only thing this seems to do is to allow steam to escape into the bathroom, and condense everywhere. With a working extractor immediately above the shower why can't the cubicle be sealed? Maybe I have missed something? maybe there's an obvious reason that showers have to be open?