Why are they more valuable to Specialists than non-specialists?
Double the focus, double the fun?
Because the number of normal slots they have are less than a non-focused specialist. So more normal slots give you better versatility.
I guess I would have thought about it differently. If I have only very few slots of X level, then the marginal benefit 1 more slot is really valuable. If, for example, I've only got a single 4th level slot, then having a high enough stat to get a second one is a big boon, it doubles the amount of Solid Fogs or whatever I can cast. If, however, I've got a ton of slots anyway, to the point where I'm unlikely to run out of sweet awesome spells to cast, then the bonus ones aren't all that valuable to me.
I view specialists as more quickly falling into the second camp. Sure, you lose out on versatility, but usually there are enough awesome spells in your specialty school that you're still casting great stuff each round, even if you don't always have the exact
right tool for the job (though some specialists can swing that, too). If there weren't enough great spells of a school to fill up a lot of your slots, you wouldn't have bothered specializing in it in the first place -- hence the quantity of Conjurers and Transmuters at gaming table and the dearth of Enchanters.