Well, people like flat pedals because most bike accidents are caused by coming to a stop and forgetting to clip out. So tending towards a flat pedal you can merely step off of seems a good idea. And on flat ground and moderate speeds it probably is. But overall it is probably not a good idea though it is increasingly common among MTB riders.
The main problem is that although it appears that people can ride just as well with flat pedals, they can't. Because you cannot pedal circles, this means that over the top and bottom the bike slows up and has to be accelerated again. While in moderate riding this is nearly undetectable, it is happening. This is especially noticeable on long climbs or hard accelerations for the next stop sign or the finishing sprint.
Older and clumsier people might find an advantage with flat pedals but if you're young and heal quickly it is better to get a set of good Look-type pedals and learn to clip in and out without having to even think about it.
As for flat pedals themselves. They coming in a variety of designs. Wearing stiff cycking shoes metal pedals with serated edges are probably better. If you're riding with tennis shoes and the like, flat surface pedals with and without spikes to hold your feet in place is all a matter of preference.
As to pedaling circles - that always incites arguments. But if you ride a long time, particularly climbing, you learn to pedal circles almost without thinking about it. If you're a racer, you may have to think and practice it some but you cannot sprint any other way successfully.
