An easy (but not satisfactory) answer could be: In mathematics, we like to extend as much as possible the properties of theorems to have a better understanding of the result.
Now from a practical point of view, it's obvious that the adaptative model is nearer the real and then provide a much more relevant security guarantee: indeed, in practice we generate the parameters of our scheme before knowing how it will be used. Let suppose there is an attack for some specific message which depends of the global parameter, a security proof in the second model doesn't avoid a such situation (and that's really bad).
Now, more generally, in some cases, it could happen the weak model is enough for practical use. But then, you have to think about the possibility that your cryptographic scheme can be used as a sub-routine of something bigger, or for other purposes. And sometimes you need the strongest property to reach your goal.
As a quick example, we can think about the fact to apply ABE to do revocation (with a blacklist): At the beginning (when you generate the global parameters) you are not supposed to know which user will be banished, then you need adaptative security to change the encryption key (to not allow banished users to decrypt).
