Does it depend on whether a person has a PhD or not?
Getting into your first quant finance role might be harder with an MFE or MSc, but once you prove yourself it becomes about politics, communication etc. Look at it this way - if after 5 years you're up for a role managing a quant team your competence on the job in those 5 years will matter more than any PhD you did or didn't do.
The reason many companies hire PhDs tends be down to a few things e.g. a PhD can work on industry projects and their experience of a PhD is much more practical. There is also a
perception when (as happens every 3-7 years) industries shift if you tell a PhD something like "you've got to re-tool and switch specialism to be marketable" they relish the challenge, while an MSc falls apart and starts counting their savings etc.
The word perception is important as if you are an MSc that could have done a great PhD, you should be able to convince someone to hire you as a quant.
I think the problem is that most math undergrads think doing a PhD would have been undergrad 2.0 where they'll be fine. They're used to having failed a maximum of 2/3 exams in their whole life but it's a complete culture change + your job is to expand knowledge, not pass a glorified memory test (face it, even in math tests that throw in problem solving that's the bulk of what they are).
If you have a job in mind already A) make sure you have better reasons (plural) to do a PhD than "getting a job" and that they are realistic (a lot of undergrads have a naive view of PhDs and professors' lives) and B) if any aspects of the PhD make you shudder then don't do it, whether it be the environment or the prospect of being in a situation few people outside of your research group understand.
It can be stressful, particularly if family and friends have some skewed views on PhDs and/or have some brain disease where they cannot acknowledge that you know what your degree is useful for (and that they actually don't understand it one iota). I've been graduated 13 years and worked in 2 industries USING my degree yet my family STILL think I don't know that a maths degree is useful in industry (not one word of a joke) and have never once considered that I got into quant finance BECAUSE I understood what the degree is useful for. The scary thing is that it's such a norm (norm-ish as some families aren't so stupid) - I'm glad I did an MSc as it only meant 1 year of that BS ringing in my ears, not 5 - think about it.