Do you need a PhD to be a quant?
The answer splits by seat, and conflating the seats is what makes this question feel unanswerable.
Where it counts
Research. Not for the credential, but for the thing the credential is evidence of: having owned a question nobody knew the answer to, for years, and having learned to distrust your own results. That is exactly what a research round probes when it asks you to walk through your own project.
For trading, a doctorate is broadly neutral. The screen is speed and judgement under a clock, and neither improves with a thesis. Several years spent not doing timed arithmetic can even leave you slower than a final-year undergraduate.
Does the field of the PhD matter?
Less than people expect. Physics, maths, statistics and computer science all convert. What matters is whether you can explain your work to someone outside it in five minutes.