Actually I'd say that philosophy is perhaps the subject that people do the worst job of learning on their own. Like, with math and science it is usually pretty apparent to people who are not experts that they are not experts and you can get pretty far just by learning basic process stuff ("this is how you solve a differential equation with this form", etc.) or facts. Almost everyone who goes very wrong here goes wrong because they are actively misled by authority figures, and lots of people with little formal background in some field are nevertheless able to talk about it intelligently because it's something they've done some reading on.
With something like history there's an easily-seen knowledge gap between amateurs and experts that similarly helps people see that they have something to gain from listening to experts. People unfortunately feel like history is just memorizing names and dates, but few people try but fail to learn history and few nonexperts think they've got it all figured out (again except when misled by authority figures).
It's fields where there's not a clear right answer that can be pointed at or clear (to nonexperts) evidence of expertise where nonexperts are most likely to go badly wrong absent a structured program that communicates that they are there to learn from someone who is qualified to teach them. My sense is that even relative to other humanities people are particularly likely to think themselves competent philosophers when actually they suck at it - you even see pretty notable scientists embarrassing themselves somewhat often.
It sounds like you are saying that people who take a shallow interest in philosophy often end up with a shallow understanding. I think that's probably true. I can also agree with the broad sentiment that it is very helpful to have someone to appropriately challenge your conceptions. I'm not sure that is a convincing argument for why a degree program is necessary. You can have a debate partner or a mentor without needing to be in a degree program.
As I see it, degree programs achieve two primary goals:
1. They provide some degree of curricular standardization and ensure you have broad exposure to the most important topics in the field.
2. They provide certification that you demonstrated some level of mastery of those topics.
Now, I think the original premise I was responding to was to the effect that philosophy is a good thing to study because it improves your critical thinking skills - i.e. something to undertake for personal growth. In that sense are those facets of degree programs really needed?
If I happen to be really interested in ethics and not at all interested in epistemology, is it a problem if I only study one and not the other?
If I am studying just for personal development, is it really important for someone to independently certify that I am doing a good job?
This sort of thing is important if the degree is a precursor to a job. If I'm a Civil Engineer and never learn about shearing forces, that could be a big problem to my employer. The degree exists so the employer is confident that they are hiring someone with all of the basic skills the degree implies. Outside of a fairly narrow set of jobs (like teaching Philosophy), I don't see where that really applies for a philosophy degree.
I do doubt that philosophy courses are doing much to improve people's GRE scores. The GRE just isn't testing much that anyone learns in college. And I bet you'd see that people who complete philosophy majors also had very high SAT scores.
Sounds like we are on the same page there.
It's causal in the sense that being good at philosophy requires the same sort of analytical skill that you need for a math degree while also being pretty demanding in terms of reading comprehension and writing.
Now you lost me. You clearly just argued that it is correlation and not causation, so I don't know why you are trying to say it is causal in any sense. Just insert the word 'not' before 'causal' and I can completely agree with that statement.