I'm a Ph.D. student in Computer Science. I originally only applied for Master's programs. I was rejected by all of the schools I wanted to go to. I eventually ended up in a good Ph.D. program, but that was largely by chance.
You're better off applying for a Ph.D. program, then bailing after earning your Master's. It's not good for the school, but it's better for you.
Your understanding of the problem is what's wrong, not your analysis. You're thinking of the Ph.D. pool and the Master's pool as independent of each other. They're not. Funding for Master's and Ph.D. students comes from the same pool, and many programs won't admit students they won't fund. So the question sometimes comes down to, "Do we admit this Master's student or this Ph.D. student?"
Ph.D. students are an investment: they eventually publish papers with the university's name, and in academic settings, the university's name will forever be attached to that person. Master's students often don't publish, and upon graduation are generally not in circles that care about pedigree.
You're better off applying for a Ph.D. program, then bailing after earning your Master's. It's not good for the school, but it's better for you.
Your understanding of the problem is what's wrong, not your analysis. You're thinking of the Ph.D. pool and the Master's pool as independent of each other. They're not. Funding for Master's and Ph.D. students comes from the same pool, and many programs won't admit students they won't fund. So the question sometimes comes down to, "Do we admit this Master's student or this Ph.D. student?"
Ph.D. students are an investment: they eventually publish papers with the university's name, and in academic settings, the university's name will forever be attached to that person. Master's students often don't publish, and upon graduation are generally not in circles that care about pedigree.