I seem to recall some places in the UK have tried changing road plus pavement into a single space and found that it does change priority: car drivers realise that they are guests in the space. Whether that continues long term is an open question.
In the UK “shared space” means “a cool name for not actually building things or just removing stuff and saying ‘done!'”. I’ve only experienced this in a housing estate where the traffic would be very low anyway. That was OK although it still has the potential to became a rat-run because the UK habit of always having two exits e.g. every road a potential cut-through.
I doubt it could work any place where one mode is inherently more dangerous / less at risk than any other and at all frequent. The old “let the lion lie down with the lamb” thing. Also won’t work well where one mode predominates. Examples: motor vehicles + bikes and pedestrians = everyone gets out of the way of the cars. Cyclists + pedestrians is the other common one we all know in the UK. If there are lots of pedestrians (and their dogs) it’s not efficient cycling, if there are lots of speedy cyclists pedestrians won’t feel comfortable.
Wiser people than me are also skeptical – read here for actual examples: aseasyasridingabike [1] [2], David Hembrow, Bicycle Dutch (with an example that seems to work), links at the CEGB.