We moved to a new area where we have lots of ancestors. I think it would be fun to see an option where we could type in a cemetary and be able to see which ancestors maybe buried there according to our family tree.
If you go to the Family Tree Mobile App and go to the More section, you will see a selection called "Map My Ancestors. This may do pretty much what you are looking for. Try it out and see what you find.
As it is now recommend, "Burial" should be the place at the time it happened; in the past. I want to be able to find my relatives' graves in the present. If an ancestor was buried in the Massachusetts Bay Colony in the 1600s and that town in now in ME, NH, or RI, I have to start "digging" to find where to drive to now; in the US, to view the grave. I suggest the instruction be changed to "Present Location" to facilitate locating a cemetery.
I've noticed that many times only the town of burial is recorded while the cemetery records are available but not recorded in the "Burial." How might recording this be addressed by Family Search?
All events should be entered using the place name at the time of then event. That is just proper history and the best way to be able to find more records. The important thing is that the burial location is correctly linked to the appropriate standardized version of the location, generally the cemetery. This standardized version is just a text version of the latitude and longitude of the location. Then all you have to do is look at the timeline map to see that latitude and longitude on a modern map. You don't have to dig at all.
For example, if someone was buried, or had any other event occur in Allen's Camp, Yavapai, Arizona Territory, United States and the event is correctly entered that way in Family Tree:
Just jump to the map to see where that is today: