Are there any other reasons for the usage of foil reflectors instead of mirrors than the ability to fold and store in small spaces? (Mirrors reflect the light more efficiently?)
When artificial lights are used in photography they're commonly diffused such as with a softbox. If the light has to be bounced off something to get it to the right place, the diffusing can be combined with the reflecting.
The difference in reflectivity isn't that great - no more than about than a stop, depending on how much of the scattered light is useful.
When using a reflector to fill the dark areas (think of a portrait using light from a window) you need disguise reflection otherwise you end up with either doubly lit areas or hard shadows still. The diffuse reflector softens the edges. If you want a portable hard reflector you can get one - stretch out a space blanket.
Chris already mentioned the softbox, and indeed photographic reflectors work similarly.
If you would use a strobe flash without a softbox (or brolly) you'd have a point-like light source which gives hard light and ditto shadows. A softbox acts as a secondary light source, i.e. it captures the hard light from the flash, and diffuses it over a larger surface. As a consequence your subject will be lit much more evenly, and shadows will be softer. No hard lines.
Same thing with reflectors, both in the studio and outside. A mirror doesn't change the light at all; hard flashlight or sunlight will remain hard. All the mirror does is change the direction of the light rays. Like the softbox a reflector will act as an area light of its own: the light from the primary source (flash or sun) is reflected as light coming from a larger area instead of a point-like source.