@Ishmael We were able to see everything we wanted so it wasn't a big deal to us.
It felt like any other guided tour we have been on in any other country.
The checkpoints were a breeze because we just stayed in the van while our tour guide got our materials checked; it would only be about a 5-10 minute wait so it wasn't a big deal.
We maybe had one checkpoint a day that we had to stop at from our journey to Shigatse, Tingri, Everest, and the same ones on the way back.
The checkpoints probably take longer in the Summer since there are tons of tourists.
We didn't see any other non-Chinese tourists outside of Lhasa so we had no waits anywhere.
Our tour guide was fantastic and became a friend so we didn't mind having him along with us, telling us all the information that we wanted to know about Tibet and its culture, and tell us where the best places to eat were.
It is okay to wander Lhasa and the other towns on your own; it is only the monasteries and major sites that you need to be accompanied by your tour guide, which is a plus anyway since the guide know all the information on any given site. The guide and driver don't have to be with you constantly, just to get you from place to place (outside of Lhasa), and in to the sites.
It was really a phenomenal trip!
I definitely recommend.