Generalist requires 200 questions in each of the top 40 tags before it is awarded; the site hasn't yet reached that milestone so Generalist badges just aren't given out yet. This requirement is not listed on the /Badges page because...well I can't really think of a good reason.
I've already requested this limitation be reduced or removed to little effect.
Yes, although a minor point I would probably agree. It's less of an issue for people with all three classes of badge because the order of the badges is always consistent (the same way that traffic lights aren't set in different shapes - we know the bottom one is always the green one), but in Stack Exchange world people can have one, two or all three types.
List of all badges with full descriptions
Badges aren't that important, IMO, and if they added indicators for everything it would just be Too Much Information (and confusing). There's no real use of knowing if a badge can be awarded multiple times. If you really want more info about something, the faq on the main meta covers it.
Also, as @Laura says below,...
Thanks to Bens' answer we can calculate when the generalist badge will be awarded
The 40th tag on UX.SE is e-commerce having 101 questions.
UX.SE is ~ 2½ years old.
If it's a linear trend and if it continues, the generalist badge will be out in the open by fall 2015. By then you will have reached almost 50k in reputation and earned 14 gold badges, 80 ...
The tag badges (and all other badges) are network wide and can’t be changed on a single site. And I think this is fair, because you don’t have to remember badge award differences between sites (as many users are members of more than one site).
When it comes to score, UX.SE are one of the best sites when it comes to answer percentage. In relation to other ...
I know this is an old question, but it hasn't been answered yet. For a few years, there is badges for asking X questions with a positive record. You need at least a total on +1 for each question that should have been asked on separate days. These three badges are very close to the limits you've suggested, so I guess this answers half of your question.