Toe clips are a compromise. They provide better foot retention and power transfer than simple platform pedals, but you don't have to think about unclipping when you stop. With plain platforms, your foot can slide off the pedal and often at the worst possible time (when you're applying high force), especially in the wet. With clipless, people tend to forget, at least once in a while, that they are clipped in and fall over with the bike. Clips don't have either problem. Also, clips are cheaper than a clipless pedal system; no cleats or special shoes are required.

The problems they do have are that when you are first starting out, clips tend to flip the pedal over the wrong way and you have to learn to flip it over with your toe as you start. And while they do help hold your foot to the pedal and provide power transfer for more of the stroke, they are not as good as a clipless pedal system for that.

Most of my bikes have clips, no straps. I've been riding that way for years and am pretty content with it.