What incentives does an advisor have to help PhD students graduate in a timely manner?

This is very simple. I care about my students, and want the best for them. Languishing in graduate school is rarely optimal for anyone. And then there is the issue of funding. For the same reason -- concern for my students' wellbeing -- it is very important to me to provide them with RA funding as close to year-around as possible. If funding starts to get tight, it doesn't help to have someone taking a luxury sixth year when he or she could have graduated earlier. I'd rather have everyone funded on RAships than have so-called "cheap labor" from senior students while junior students are forced to TA.

If the question is referring to why even a sociopathic advisor would want his or her students to graduate on time, there is some prestige in having students graduate quickly and move on to good positions, and some shame in having students in their sixth, seventh, and later years.

The incentives vary strongly by location, although I think the usual driver is monetary. For instance, in Germany, it is difficult to be employed as a PhD student at a single university for more than six years (following the completion of the master's degree). Moreover, because the recruiting of PhD students is often done "from within," if a professor becomes known for not graduating students, it can hurt long-term recruiting. (Also, DFG funding typically can be extended on a single project for five years.)

For US professors, there may be an expectation of graduating a certain number of students as part of the requirements for being granted tenure. However, I think the bigger incentive is that beyond a certain point it becomes too difficult to keep finding funding for a long-term student.

At least at the university i'm at in the UK (and I belive this is true in the UK more generally and is pushed on them but some national body though i'm not sure offhand which) there is a 4 year limit on regular full time PhDs that can only be extended in exceptional circumstances. Students who fall off the end of said limit reflect badly on the department. Things that reflect badly on the department tend to result in the head of department having a go at the indidvidual academics who caused it

I belive this came about precisely because so many PhDs were dragging on for years and it was considered desirable to put pressure on both students and academics to finish up the PhD and move on.