ZLC Center Controller reported an aircraft descended below a crossing restriction and did not complete a required procedure turn on the ILS approach at WYS airport. Controller stated the approach is often not flown correctly and recommended a straight-in option be added.

Narrative

I cleared Aircraft X for an ILS Approach at WYS initialing over SABAT. The transition in not a straight-in transition. The published altitude after SABAT on the transition is 11;500. After I changed Aircraft X over to advisory frequency; they proceeded to descend to 10;000 after SABAT; 1;500 feet below the published altitude; then intercepted the localizer and skipped the procedure turn altogether.The ILS Approach at WYS needs an IAF that allows for a straight-in (noPT) approach. The current ILS Approach is grossly inefficient and is incorrectly flown by airline on a regular basis. While descending to 10;000 on the SABAT transition is still at my MIA; the pilot has no altitude guidance below those altitudes published on the approach. I have reported this in the past. At the time (pre-COVID) there were communications taking place to add a fix (perhaps FEVIP) to create a straight-in option. Pilots were also briefed that they were flying the approach illegally. It appears we are back to square one with no changes made to the ILS Approach and pilots flying it incorrectly.