Actually, most doctoral programs in the US in most fields are open to those with only a bachelors. It isn't a few. It is nearly all. There are several reasons. Probably the most important, though perhaps not stated, is that the faculty gets to look at a student for a while before taking them on as a dissertation advisor. But there are many other considerations including how the university is managed overall.
Most programs start with advanced coursework giving a broad education in the field of interest. This leads to required comprehensive exams in the major subfields. Once past that, perhaps in the third year, serious research toward the dissertation begins. It may be that you earn a masters along the way, sometimes just for filling out paperwork and sometimes after a minor thesis. But this isn't necessary for everyone.
Most universities also have masters programs intended for those not interested in a doctorate, perhaps because they want industry positions, rather than an academic career. These are normally funded by the students themselves through tuition and fees. On the contrary, doctoral programs are normally funded differently through Teaching or Research Assistant positions, which normally include nearly all fees as well as a modest living stipend.
The advantage of the doctoral funding arrangement is that most major doctoral programs also have a large undergraduate population and the TAs help maintain the lower level courses by grading and by holding regular small group sessions for students whose courses might be very large (hundreds of students). They make some personal contact possible to ask questions and get feedback. Without TAs the faculty would need to be much larger, leading to a much different financing issue.
Note that my experience is Math and CS. In those fields, most entering doctoral students haven't gone to R1 (major research) institutions as undergraduates and actually have little significant research experience. This is due to a lot of factors, but the US undergraduate program is very broad with a math major taking courses in writing, history, philosophy (perhaps) and several others. There is little time, even in a four year program for research and few reach enough experience in their field to be able to do anything but poke a bit at research.
Even masters programs in the US, which are often just two years, are too short for most students to do serious, leading edge, research. Some masters programs are just advanced coursework, such as a beginning doctoral student might have, and some require a thesis. It isn't likely to be leading edge, however.
There are some exceptions, however. A few programs run closer to the German model where students are expected to have a masters on entry and are immediately assigned to a lab where they are given some "research adjacent" tasks that will hopefully lead to a doctorate. This isn't the norm, however.
Where a broad based education, validated by comprehensive exams, is the expectation someone who already has a masters might actually be at a disadvantage if their masters didn't provide that broad base making it possible to pass those exams, which can be very challenging and are normally based on advanced, not elementary, material.
I don't see a lot of relation between this model and global rankings. It is an alternative model that works. Funding of US research universities is very varied. Some is from the states that run the university. Some is from foundation grants. Some (a lot) is from tuition paid by students. But the TA system helps keep costs down due to the modest nature of the funding compared to the salary and benefits that need to be paid to research faculty along with the cost of facilities in general.
International students with bachelors are admissible to such programs on the same basis. Some might even have an advantage since the bachelors program in several places is more field-intense than is typical of a US bachelors. And with a masters you might still need to deal with comprehensive exams.
