If you are riding a bike leisurely at say 12 kph down the street, clipless pedals aren't going to be useful and might even get in your way. If you are riding in traffic at 30-40 kph, then they can literally be a life saver. Over 90 RPM it's hard to keep your feet on the pedals. So if you need a sudden burst of speed when in a low gear, then this will make sure your feet on on the pedals. Also if it's raining and you hit a pot hole, for instance, your feet will be on the pedals. This really helps in keeping control.
If you've never tried them before, I highly recommend it. I never once fell off my bike due to clipless pedals, although some people do. Even though some people fall off when they first start, I've never met anyone who preferred flat pedals after trying clipless for a while.
The one place I would not use clipless pedals is if I was doing a lot of off-road stuff. I know some people use them anyway, but if you need to put your foot down regularly, it's pretty difficult IMHO.
The questionable part is, do people apply pressure on anything but the down pedal stroke when they're seated, and riding normally. At least for me, the answer is no.
But they're still nice to have, especially on a single speed or fixed gear. And for fixed gear, flat pedals are unsafe. They give you a lot more control.