Shutter lag in new cameras actually is nowhere near as bad as it used to be, although when today I ran out of film in my Zenit EM and switched to my digital snapshoot camera (which is actually a pretty decent camera), I found it quite hard to adjust to autofocus, shutter lag, and the unfortunate fact that you cannot see much in the LCD if shooting in a sunny day (I very rarely use it now that I've rediscovered the joys of film).
However, digital clearly has advantages for the average snapshooter; you get immediate results so you can see if you've goofed or show off the picture to everybody on it just after it's taken (call it names if you like but that IS great, that's what made Polaroid popular in the first place), it's extremely portable (simple digital camera fits very easily in pocket, and few 35mm cameras do -- with notable exceptions, of course, like the most venerable Olympus XA), it's cheap (digital P&S cameras start at pretty low prices nowadays), and then you also save 'cause you don't have to pay for developing film, and, probably most importantly, the picture is already digital, so you don't have to have it scanned in anymore.
Digital pictures fit the current life just fine: you can easily share them, you can store them on a CD and then just pop in a computer when you want to show them, instead of keeping a large album. Everything is fast and portable, just the way people like it. Yes, they are very temporary and might have serious archival problems. Of course, you can print them out, but few people do. But again, most people today can live with it. The thing to remember is thar we live in an increasingly throw-away society. Things are so cheap that it's cheaper to throw them out when they break than to repair them. And this menthality extends to other things, such as family photographs, as well. The adoption curve of digital very strongly suggests that people actually can accept all the inconveniences of those cameras, so it's a bit useless to suggest how much better off they would be with a film camera. Of course, it's always possible that this is just a mass fad and people are buying useless cameras just because everybody else is.