BOI TRACON Controller reported lack of obstruction displayed on RADAR display and DVA procedure change resulted in an MVA violation and a CFTT event. Controller also stated to select correct map would take too much time and attention from monitoring that radar display.

Narrative

Aircraft X was on published missed approach climbing to 080. As the aircraft neared a 5000 MVA; I told them to leaving 5000; turn right heading 230." They neared the next MVA of 065. I observed them making the turn; and their blue dot of the fused radar beacon was on the line of the MVA. They completed their turn and second approach and landed safely.Recommendation:I was told that if I had tried to find the MAP that displayed an obstruction of 034; I could have instructed the aircraft to turn; upon immediate contact. Because the obstruction is not permanently displayed; I would have had to take the time; heads down searching out map list of at least 50 maps trying to find the right map. The lack of displaying a map of an obstruction well below the aircraft is the reason for a MVA event? Not allowing missed approach aircraft to use an established diverse vector area is by far the most ridiculous change the FAA has done in the last quarter of a century. The recommend I have to the entire FAA is to reinstate that we are allowed to use the established diverse vector areas for missed approach aircraft that area established in a climb. Locally I have already told the ATM (Air Traffic Management); I believe the obstructions should be on the main maps that are always displayed for this purpose."