Good question, I know the GMAT is alway a major area of concerns for many candidates so think you have posed some interesting points. So please find a few of my thoughts on some fo the questions you posed below:
-How do admissions assess the GMAT scores?
They assess it as one of many "data" points in a candidates profile. The value with which it is used it largely based on the candidates profile and how it fits overall into their view of the makeup of the candidate. It is important just like your resume, essays, and GPA
-Do the have more focus on quant vs. verbal?
Again, it depends on the candidate most tend to believe the quant section is more important but it really depends on the applicant. A career investment bankers performance split vs. someone in non-profit will be looked at pretty differently. Their evaluation will work in concert with how your overall story reads
-Do they just want the highest score in order to boost their rankings?
No, I do not believe this. Schools could literally fill entire classes with students with GMAT scores above 750 to boost these numbers but they do not and the reason is most top schools genuinely want to admit people not just numbers and they understand the value of evaluating the entire package not just a few high numbers. Now the numbers are important just not everything when considering admissions
-Do they just see if you meet a certain threshold i.e. 650+?
I do believe there are certain scores that signal a certain level of aptitude, but most schools don't have a definitive cut-off, we hear stories every year that validate this. If a guy like Mark Zuckerberg applied to b-school this year with a 550 GMAT would schools automatically ding him? No, of course not because the rest of his package would probably be very compelling, now this is clearly an exception but it does inform aspect of the process.
Overall, I would say the GMAT is not going anywhere as an evaluative point, so if you're planning on applying to b-school I would just accept that and try and do your best. There will be little value and fighting this aspect of the process outside of wasted time on your end that you could spend working on your application.
Hope this helps!