Background: I have a math Ph.D. and am working as a statistician in industry.
I'll try to address both the general question you ask and your specific situation.
M.Sc. vs. Ph.D. in stats in general
This quote of yours is key:
I do not believe PhDs would guarantee job security, higher wages, or happier careers.
And you are right about this. A Ph.D. won't guarantee any of these.
If you do a Ph.D., you will end up with a different qualification than with "only" an M.Sc. In doing a Ph.D., you will be spending multiple years thinking up new methods or algorithms. You will become an expert on an (admittedly small) topic, which you will know more about than your advisor. In contrast, in doing an M.Sc., you will learn a lot of different techniques and apply them, but you won't develop new ones. (Some M.Sc. students do just that - exceptions exist.)
What does that mean for your job prospects? If you are looking for a job as a "consulting statistician", "data analyst" or similar, an M.Sc. will usually be enough. Employers may balk at hiring a Ph.D. for such positions for multiple reasons:
- Ph.D.s usually ask for higher salaries
- Ph.D.s are older, possibly less flexible (families) than entry-level M.Sc.s
- Ph.D.s may feel underchallenged and try to leave for more interesting work elsewhere
- Ph.D.s may be specialized in one field - but an M.Sc.'s knowledge of multiple methods is more recent
So with a Ph.D., you would be applying for more "conceptual" positions, where you don't only apply your knowledge, but actively create new statistical methods to solve problems.
There are more jobs out there that require applying known methods than creating new ones.
You may be lucky and find a job opening that requires a Ph.D., or (even better) one that matches your Ph.D. research interest. (I wouldn't count on this last possibility - research is so specialized these days that it is rare to find a position in industry that closely matches what you did in your Ph.D. career.) If so, your Ph.D. pays off. If not, you may be in for a long search, or you may need to work for lower wages, and still need to convince an employers that he is better off hiring you than a new M.Sc. graduate - at the same wage. If this happens to you, you will definitely feel like the Ph.D. was a waste of time.
Overall, I would only recommend doing a Ph.D. if you are passionate about it, if you genuinely want to devote three to five years of your life to research. Don't do a Ph.D. for the career value if you plan on leaving academia. It likely will be a step backwards in terms of lifetime earnings or your career progression. (Around me, I see no correlation between having a Ph.D. and job security or higher wages - I can't judge the happiness of my colleagues' careers.)
Your specific situation
I have a bit of family pressure to get a job and work to build income.
It seems like an unwise choice to pursue a PhD and graduate at age
35-36 without work experience and having to start earning income.
... On a personal note, I am quite disenchanted/burned out with higher
I see a lot of skepticism about doing a Ph.D., and much focus on your alternatives. I don't see anything indicating you would love to do research for research's sake. (Please don't misunderstand me: I'm not saying you are lazy. I am pointing out what your priorities seem to be, based on your question.) Compare this to my recommendation above.
It does not seem to me that doing a Ph.D. would be a wise move for you.
Nevertheless, we can't usefully help you a lot with your decision. I'd recommend you talk to people who know you and your specific situation.
This and this earlier answer of mine my be helpful.