That not true at all. The name of the university can only get you so far. For example, if you have a climate-related degree, can you really compete with Stanford CS majors for a SDE job? Or with ME majors for a product design position?
IMO if you get into Stanford and can pay for the degree, it would be a waste to spend it in a major like that unless you're really passionate and have very specific goals.
"So, basically, investment banking or data science"
Well, those are definitely not "whatever you want".
For this specifically: Yes, depending on your extra curricular activities and interests. And if it was a graduate degree, then yeah almost certainly.
Thankfully there are fewer Stanford CS majors graduating than there are SDE jobs available.
> What do your do with a degree in climatology?
I write code, ironically. I'm in the camp that believes degrees aren't _totally_ about what you learn but more about advancing your reasoning and thinking skills and learning how to interact with people (not to say you don't learn anything in school, you definitely do but IMHO it largely depends on what you study).
This all goes under the rubric of 'planetary sciences' of which 'earth system science' is a sort of special case. Also means you could work at NASA on Jupiter's moons etc.