There's a bit of an inaccurate presumption in the question itself, or anyway ambiguous wording. That is, some assumption of causality...?!?
As a mathematician, I do not think of PhD students individually or collectively as assisting my research program so much as doing teaching work that I don't have to do. Even my own PhD students, while stimulating to talk to, do not "help" my research program. Perhaps this is contrary to mythology. Although more-experienced TAs (teaching assistants, in the U.S.) are generally better at their job due to that experience, that level of proficiency is attained within a year or two of beginning the role. That is, in my sort of situation, there is absolutely no motivation for faculty to delay completion of PhDs. Indeed, as @roboKaren comments, there is some pressure from higher-ups to improve "stats". (That is, in terms of TAs, we cycle them through at a certain rate, so there're always roughly the same number to do the TA work. Shortening or lengthening the cycle time would accomplish nothing, and we have no motivation to do so.)
Is the supposed issue about people leaving the program? This is a very complicated question, considering that it might be entirely reasonable to leave a program if/when one discovers it's not what one thought. Should we brow-beat people to stay? Bribe them? True, being nasty to try to "drive out weaklings" is incivil, but I don't address that possibility.
If the question is about the "drop out rate", then it is probably impossible to answer usefully. If it is about time-to-completion, some useful things can be said.
This simplifies the question to two very different ones: about my interest in colleagues' students finishing faster/slower, and about my interest in my students finishing faster/slower. Apart from general humanitarian/professional-ethical concerns, I have no interest in the arc of other peoples' students, as it is really not my business. It is true that my perception (based substantially on two stints as Director of Grad Studies in Math) is that some PhD students and their advisors devolve into an unproductive, uncommunicative relationship, with "blame" not clearly assignable, but which creates enormous difficulties in completion. E.g., if either party is naturally non-verbal (despite the seeming ok-ness of this in math, ... which is not the case, actually), there is a potentially fatal problem. If there is a misunderstanding (from either side) about the context, origins, degree, and sense of the alleged "novelty/progress" of a thesis, this can be a huge obstacle.
For my own students, I try to arrange a thesis project that will optimally
use the talent, energy, background, etc., in the time fully-funded by the department as TA (not counting on RAs (research assistantships), fellowships, etc). My thinking is that one's clock really, really starts once one is "out the door", so taking a sixth year instead of just five may be well worth it. But if/when someone says they want to finish more quickly, a suitable project can be chosen, up to a point: usually, there is a misunderstanding, a misguided prior belief that, indeed, somehow, faculty or departments are conniving to delay degree completion. :) "If only they'd get out of my way so I could do my research...!?!" ... overlooking the point that all the "required" stuff is meant to assist that (nevermind the common stylizations and distortions and misunderstandings).
So: incentive for quicker completion than the funded period? None, on scientific and educational grounds. On bureaucratic grounds, there's an ever-hardening soft cap on funding, which is a good reason to get people out the door... even though this soft funding cap is meant in practice primarily to avoid funding "eternal grad students" who make a bit of progress but either can't finish a PhD-worthy project or who are unhire-able for some reason (e.g., inability to speak in English, in the U.S.).
So, while my experience as Dir Grad Studies in Math made me unhappily aware of others' foibles, I don't think there's much motivation in mathematics for faculty to delay PhD graduations, and only a little to accelerate it. But faculty aren't the obstacle, in most cases. It's just that the U.S. undergrad system under-prepares people for grad school, so there're two or so years of basic coursework necessary to be even marginally literate, and then becoming aware of the basics of any fragment of modern mathematics can (obviously... though people in CompSci seem to have a radically different epistemological mythology) take a year or two. Unsurprisingly, quite a few people discover that "math" is not what they thought it was, given that U.S. coursework typically is at best very-early 20th century stuff, giving no inkling of mid-to-late 20th century stuff, apart from the not-really-contemporary-research, somewhat delusional (inevitably fairly contrived) "REU" (research experiences for undergrads) episodes. Given the popularity of REUs in the U.S., I'll not comment further on the alleged virtues-or-not... apart from agreeing that, yes, it is good to spend some time hanging out with other same-age kids who really like math, and not being in the usual stodgy classroom situation...
So, if "completion rate" means completions-per-admission... well, that's a can-of-worms, all the more for programs (such as ours) which try to be imaginative in visualizing the success of some students who do not necessarily have the traditional trappings of "success", but seem to have sufficient interest and talent. Gambles! If we'd be taken to task for not gambling on sure things... ?!? And a similar analysis applies to length of time to completion: pressuring people or limiting them to finish more quickly could induce more "failures", rather than "coerce" faster success.
Again, I feel that the question itself is predicated on a misunderstanding of why it is not so easy to get a PhD... but maybe I'm just old-and-tired. :)