Conversely, there are also often advantages to using an EF lens on a crop sensor as you can benefit from the "sweet spot" effect whereby vignetting is reduced and overall sharpness can be increased if the lens is slightly softer towards the edges.
Not really. If you want to look at it that way, then an EF-S lens is like an EF lens with all the extra glass cut away so you only have the sweet spot left. Hence the savings in size and weight. The best EF-S lenses are at least as sharp as EF.
Yes, it starts at less than 60mm
That's a cracking little lens, and another good example of how the smaller format of crop benefits lens design. Compare these two:
EF-S 55-250mm, f/4-5.6, IS, 390g, 108mm long, £220. In terms of field of view, it is equivalent to 88-400mm on a full frame camera. Canon makes an EF lens close to that configuration in the 100-400mm L, f/4.5-5.6, IS, 1,380g, 189mm long, £1,300.
Okay, one is a plastic consumer lens and the other a pro-spec L, but I think the differences are pretty convincing. However, there are downsides to crop format - it is smaller than full frame (obviously!) and that will always make a difference. But if you don't have a camera to take advantage of that, then why carry the penalty?
It's just another way of looking at the options