A master’s program is never going to hurt you, and is probably going to help you in admissions. But unlike a lot of humanities fields, you don’t need a master’s degree in psychology to get into a PhD program. You can get the things you really need (research experience, developing your research statement, letters of recommendation) from working as a research assistant or lab manager/coordinator for a few years after your bachelor’s degree. Since master’s degrees in behavioral science are rarely funded, this is likely to be much cheaper.
By all means, get a master’s if you really want to - particularly if you have interests in intersecting fields (like public health, social work, other social sciences, etc.). A master’s is certainly an excellent and well-structured way to gain that experience. But that’s not the only way to do it, and it’s certainly not the cheapest.
I definitely agree with the math and especially the writing skills. Writing is SO important in graduate school and beyond, and I come across so many students, early career PhD students and even PhD graduates with bad writing. I’ve got experience hiring folks for industry research roles and your writing is definitely something we look at. Life in the program is just really much easier if you have strong writing skills.