NCT TRACON Controller reported pilot failed to fly departure procedure entering a higher MVA; resulted in a CFIT event.

Narrative

I was working departures. I was in the process of vectoring one departure around parachute jumpers over E16; another departure to NTELL; and I believe a VFR or two on frequency. Aircraft X checked in with me; I verified the altitude and they stated they were on the SJC3 departure. I advised radar contact. As I watched the climbout; I observed Aircraft X turn eastbound over or just north of the VOR; which is earlier than the departure calls for as it should be 1.8 DME north of the VOR before the turn starts. I immediately issued the low altitude alert and advised the pilot to expedite the climb. As he was already in the turn towards a higher MVA (Minimum Vectoring Altitude) ; I knew that I would be unable to turn him northbound up the valley without him entering a higher MVA with a roll out of a right turn into a left turn again; in fact it would have out him closer to the mountains than the right turn they did to join the radial southeast bound. The pilot expedited the climb; I observed his climb rate and that they joined the remainder of the SJC3 procedure in a safe manner; which kept them away from terrain further to the East. And the next controller asked for Aircraft X on a 180 heading. Aircraft X was below the MVA still and there was traffic on final for SJC; so I told the next controller it would be a minute. As the pilot was reaching the 037 MVA; I turned Aircraft X southbound and sent them to next sector. They inquired for a phone number; and we had ZZZ Tower issue the brasher warning to the pilot when they landed for the pilot deviation.The pilots failed to execute the procedure properly. Unfortunately; with rapidly rising MVA 's and terrain out of SJC; there are limited options available to observe and correct a situation of an early turn. If Aircraft X were to continue eastbound; they would encounter higher terrain. However the most common occurrence of deviations on the SJC3 are missing the 1.8 DME limitation on the turn off of SJC; which I believe is actually primarily for noise abatement. A call from the Tower could have helped if they had seen an early wings up situation as they shipped Aircraft X or soon after. But there is no evidence that would lead me to believe that they observed this situation at all; as it was after the initial check-in that I observed their turn as occasionally radar takes a minute to indicate that on initial contact in fusion. As soon as I saw it; I took action and knew turning back towards a lower MVA was unfeasible to keep the Aircraft X the furthest from the EOVM (Emergency Obstruction Video Map) depicted terrain. I ensured Aircraft X did not continue eastbound past the radial towards the terrain to the East and complied with the rest of the departure while issuing the low altitude alert. I could not turn south down the valley further as LICKE had a final and Aircraft X initially was not climbing fast enough to avoid the traffic on a 3 mile final to SJC. When safe to do so and when I knew Aircraft X would be at the 037 MVA when starting the turn; I issued to vector southbound and moved on with the traffic. I believe the procedure is clear; but pilot deviations on non-RNAV departures seem to be increasing at a rapid pace. I believe their is beginning to be a breakdown in training as classic non-RNAV departures are not as common as they used to be. Pilots are either not hand-flying the aircraft or not reading procedures appropriately. This is becoming a major issue and it needs to be addressed on the pilot and air traffic sides. Pilots need to fly published procedures. Air Traffic may want to look at either Vector Departures for non-RNAV departures to simplify the departure and alleviate confusion; or design RNAV departures of older procedures so the new generation of pilots can comply as their grasp of older procedures is clearly declining. The status quo of numerous pilot deviations on these procedures is clearly unsafe and putting all controllers in difficult situations as theyhave to evaluate all of these situations on-the-fly and make the best decision they can with the information available at the time while also working normal traffic flows to keep all users safe. This needs to be addressed on all sides to enhance safety and get us back to the levels we saw before 2020.