If person ha no particular profession in mind (a born rich trust fund baby, for instance) but did have an interest in science in general but no overriding interest in any field, would a “science” degree be worth pursuing? Just out of general curiosity?
If you just want it for your own personal edification, it doesn’t much matter what you major in: You can take serious, meaty classes while officially enrolled in any major whatsoever. That said, though, a General Science major would make it possible for you to completely avoid all of the really substantive classes, which is something you couldn’t do in a more specific major. And the high-end classes will also generally have a lot of prerequisites, both official and practical, meaning that it’s really hard to find enough time to reach the high-level classes in multiple different scientific fields.