A longitudinal study collects data from the same subjects over time. If one is studying language development and intelligence, observation of the same subjects, usually very young children, affords a researcher a way of seeing how language develops and a way of gathering information about intelligence, which may or may not develop over time, something we would all like very much to know. If we want to know how language develops, we need to see it developing. If we want to know if intelligence develops or is static, we must observe it over time.
Non-longitudinal studies are certainly done in these areas, though. For example, one might look at a "snapshot" of children from different environments to see if those environments affect language development. Similarly, this approach is used to study intelligence.
In these areas, as in any other area, the kind of study chosen is a function of one's inquiry. What do you want to know? What is your hypothesis? Longitudinal studies are time-consuming and costly, and when they involve children, they are even more time-consuming because special precautions must be observed. Nevertheless, sometimes the nature of the inquiry necessitates a longitudinal study.