In the US, most Ph.D. programs accept far fewer students with master degrees compared to students who just graduate from college with a bachelor. Why is that the case since master students are supposed to have more background and maybe more research experience than students who just graduated from college?
I'm not sure that your basic premise holds. What you've stated is not common knowledge, and you don't give any particular source for your numbers. More importantly, you haven't answered @NateEldedge's question about total numbers vs. acceptance rates.
Based on my own anecdotal experiences, however, my guess would be that the actual circumstances are this:
- Students with a Masters are more likely to get into a U.S. Ph.D. program than students without a Masters, for exactly the reasons that you suspect.
- Most students interested in a Ph.D. program, however, apply directly without bothering to get a Masters first. As a result, it may well be the case that most U.S. Ph.D. students do not have a Masters.
The underlying reason that would cause such an apparently counter-intuitive situation is that in the U.S., it is typically the case that a Ph.D. and a Masters are both terminal degrees that serve different purposes. A Masters is frequently a focused collection of coursework in support of one's profession, whereas a Ph.D. is an apprenticeship into the world of research. As such, most U.S. Ph.D. programs do not require or expect applicants to have a Masters, and there is often little incentive for students inclined toward a Ph.D. to delay and acquire one, unless they have some particular reason (e.g., they aiming to shift fields, improve on a past poor record, or escape the effects of a poor undergraduate institution).
Note however, that in other parts of the world, like Europe, Ph.D. programs are organized to assume that students have already acquired a Masters, and in such programs it is the case that nearly every Ph.D. student will have a Masters.
Most of the students in the US who are in Master's programs in the arts and sciences are only in these programs because they failed to be admitted to PhD programs with their Bachelor's degree. Generally speaking, being in a US Master's program is by itself a sign of weakness.
While some students do become significantly stronger over the course of their Master's programs, generally speaking, students with a Master's degree have less innate ability than students who are admitted directly after a Bachelor's degree. They may have more knowledge and experience(*), but this is usually easily made up for in a year or two of study. (There are exceptions, and it's quite easy to spot them from letters of recommendation, but you're asking a statistical question about numbers overall, not about specific individuals.)
Foreign students who might not have had the opportunity to be directly admitted to PhD programs immediately after a Bachelor's are evaluated differently.
(*) Actually, someone with a Master's from my department usually knows about as much as someone with a Bachelor's from a top university, and is significantly less capable.