I just want to add a few things to this
I have a few thoughts, so for the sake of simplicity, I'll just bullet point.
1. Why MD/PhD is funded, and MD isn't:
1) Unlike students who go through MD only programs, MD/PhD students are generally prepping themselves to make far less money once they graduate. In general, clinical work pays much more than science, and the more time a physician scientist spends in lab, the less they can expect to make per year. Because programs are so long, very few people would opt to earn both degrees if they knew they would have so much loan money to repay on a lower salary.
2) Like other graduate students, MD/PhD students provide cheap labor for labs at their schools. It would be unreasonable to not pay PhD students for their time, and the added pay/tuition waver during the MD portion is necessary because many students do PhD work during their MD years in the program. Again, it's also an added incentive for taking time for those extra years.
3) As this poster said, the government has an interest in training physician scientists who can participate in translational research. Who better to do research targeting clinical problems than those trained in both areas?
In general, the PhD portion of a program is anywhere from 3 (rare) to 5 years, depending on how lucky a student gets with his/her research. MD/PhD students generally finish their PhDs more quickly than PhD students, but this is mostly because they may take graduate courses or complete rotations during their MS1 and MS2 years. This leaves more time for thesis work once they hit the graduate years, and lets them hit the ground running.
Note that time will vary depending on the student, the PI, and luck. PhDs are unpredictable and have no definite endpoint.
Also, the issue isn't so much that board scores expire...the problem is that some states require all licensing exams to be taken within a certain number of years of eachother. Many states grant exemptions for MD/PhD students, and others don't restrict this at all.