In practice, sure, that's fine. As a career choice, I actually want to get some research done, so I'm likely to take an approach similar to that of a professor at my school.

The thing is, I'm starting to hear people making all sorts of claims like "Those people aren't really doing science," "That researcher isn't going to get anywhere with his approach" and I want to know when I should find those comments credible. I get curious, you know?

The problem with this is that there are a nearly infinite number of hypotheses to explore, and we can't examine them all. So we need some kind of criteria, even something as simple as k-complexity (for hypotheses) or ease of use (for models and methodologies). A good exploration of this idea can be found in chapter 7 of this introductory book.

This seems reasonable to me. On the one hand, every available approach to an open problem is going to be deficient in some way, but on the other hand it's difficult to figure out the missing insights if you don't know what insights already exist. The best way to deal with this is probably to just study lots of different things (everything, if possible).

This also probably pertains more to theoretical science. Empirical science seems like it operates more in the realm of "what kinds of facts have we not gathered that might be important?" rather than necessarily talking about theoretical insight that could be gained.

Ugh. Science methodology is hard.