At least in the U.S., ILS is popular because it is popular. It's relatively cheap to install and operate, the receivers share technology with VOR, and it is already installed everywhere. Momentum (and cost of replacement) has a lot to do with the failure and success of navigation systems.
MLS requires new hardware on the ground and in aircraft. The FAA tried to roll it out in the U.S. in the 80s, with a goal of replacing ILS by 2010, and utterly failed. The equipment was expensive for aircraft and ground facilities, and the cost of developing the approach procedures was high, as well as each approach needs tailored antenna programming (ILS is reasonably standardized). The adoption rate was low and the benefits (better arrival area guidance, better accuracy in some cases) were duplicated by the much cheaper GPS.
Precision GPS (LPV or LNAV/VNAV approaches) only appeared with the development of the Space Based Augmentation System (SBAS), also known as the Wide Area Augmentation System (WAAS). Augmented GPS has higher vertical precision and allows a single navigation system to be used for enroute, terminal, and precision approach guidance, a huge cost savings. The relatively new Ground Based Augmentation System (GBAS, originally called LAAS) adds high precision approach capability bringing GPS approaches closer to ILS and MLS.
PAR exists, but you may misunderstand what it is: it is a controller staring at a radar scope and issuing pilots instructions. It's stressful for pilots and controllers and very time consuming. Outside of military facilities you would be hard pressed to find a place to practice a PAR these days, at least in my experience.
In order of precision, high to low:
- GPS with GBAS (uncommon)
- GPS with WAAS (common, aka LPV)
In order of (estimated) total cost, high to low:
- MLS (very expensive install + unique approach design + maintenance)
- PAR (relatively cheap install + costly workforce; educated guess on my part, could be cheaper than ILS?)
- ILS (expensive? install + simple approach design + maintenance)
- GPS with * (no install, simple approach design, no obvious maintenance)