After reading all the questions and answers in the comments (including my own), I think I finally have a good enough understanding of your situation to answer.
And the answer is - in your case, fiberglass insulation will help, but you have to be careful about how you apply it.
Why?
The point of insulation is to create a thermal break that prevents the transfer of heat from one space into another. You get heat transfer through a roof or a wall because hotter side (whether you're inside or out) warms the wall of the cavity, which in turn warms the other side of the cavity. If your wall is closed on both sides (the norm), that warmer air within the cavity then warms the cooler wall on the other side and so forth.
Insulation serves to reduce the ability to heat the air in the cavity - it's basically a spun glass thread (hence the fiber - glass) which is much less thermally conductive than air, and the spun texture creates lots of little air pockets within the fiberglass, so it's much harder for heat to move from one side of the fiberglass to the other.
Now this thermal break works whether or not the cavity is closed up, which is why you see fiberglass or loose fill insulation (cellulose) in attics sitting on the attic floor (aka the ceiling below) without any covering over top. So - IF you put fiberglass in your garage ceiling, you will improve the thermal resistance of the roof, and help keep your garage cooler in those hot NV summers.
HOWEVER - here's the danger - if you apply the wrong kind of fiberglass or apply it the wrong way, you're going to destroy your roof over time.
Why? The moisture trap.
In your case, the biggest risk is trapping moisture up between the ceiling rafters, which will eventually rot your roof from the inside.
Right now your roof isn't at risk of a moisture trap because the space is completely open, so moisture doesn't get stuck anywhere against the roof, it dissipates into the garage. However, if you put the insulation in the wrong way, since your garage roof isn't vented via soffits you'll create an enclosed space into which moisture will get sucked in and get trapped, creating a hot damp jungle like space right against the plywood of your roof, and boom - mold, bacteria, destroyed roof.
So - in your case - use UN-BACKED insulation - that means NO paper on either side - and insert into the cavity. Do NOT secure the insulation in place with sheets of plastic, you need to secure it in a way that (ironically) allows plenty of air flow. You could secure it with thin strips of wood placed about a foot apart, or something like that, or you could try stapling the fiberglass to the rafters... dunno how well that will work. In other words, getting it to stay put without trapping moisture is going to be a pain - but it WILL help insulate your garage.
All that said ... I would recommend you just jump right to spray foam. Why? Because spray foam creates the moisture barrier where it needs to be - right against the plywood of the roof - so there is no way for moisture to become trapped (no pinholes to suck it in and hold it) - AND you won't have a hard time just getting it to stay put, because it sticks on its own, unlike fiberglass. And since there's ZERO air flow with foam (unlike fiberglass), the insulation quality is better.
So yes you can fiberglass - but I wouldn't even bother with fiberglass in your case because of the trouble to install, the lower R value, and oh yes, its going to look ugly however you install it cause it's going to sag. (Stupid gravity...)
Spray foam insulation is a petrochemical product that is mixed on-site and blown with a blowing agent. The actual process is not great for anyone's health, which is why applicators wear protective suits. It is also exothermic, and if done incorrectly can cause a fire (rare). Additionally, if mixed incorrectly, or even in a small percentage of cases, the foam will offgas nasty stuff for a long time, rendering the house uninhabitable. I must stress that these cases are rare, but they do happen. Furthermore, fully-cured spray foam is flammable at elevated temperatures and will char and emit smoke at typical household fire temperatures.
Are there better insulations out there than spray foam? Absolutely. Spray foam is about the most expensive insulation you can get, and it is terribly mis-used most of the time, applied where its benefits are wasted. For insulating walls between stud cavities, wet-sprayed dense-packed cellulose, sprayed fiberglass (under the brand name "Spider") or mineral wool batts are better choices. For turning an attic into conditioned space, installing rigid foam boards above the roof sheathing is the preferred approach if already re-roofing. If that's not an option, then you can fill the spaces with the aforementioned choices of cellulose, fiberglass, or mineral wool batts, as long as you 1) create a ventilation channel of 2-4 inches in the rafter bays below the roof deck, 2) install a ridge vent and soffit vents that allow every rafter bay to be ventilated, 3) use an interior-side smart vapor retarder membrane such as Intello MemBrain (note: NOT a vapor barrier like polyethylene sheeting), and 4) you finish the assembly off with drywall, being careful to make the drywall layer as airtight as possible. Alternatively, you can detail the vapor retarder membrane as an air barrier and skip the drywall or use non-airtight finish materials like tongue-and-groove pine boards or something.
Best Answer
Polyurethane foam is an excellent insulator, and it needs no added vapor barrier. Depending on your climate and local building authority requirements, you will need anywhere from 4 to 7 inches of foam. The remaining airspace does not need to be filled. It will help prevent your new ceiling from getting wet from inevitable condensation. Alternately, you could install baffles against which to spray the foam, creating an air gap below the roof sheathing and creating a sort of cold roof, if that has any benefit in your climate.
The foam is such a good vapor barrier, you will need a plan to remove excess moisture from your house. Frequent use of bath and kitchen fans may be adequate, depending on climate and remaining construction. You might consider whole house ventilation through an air to air heat exchanger or similar.
If you are removing the ceiling, you can pretty much use any type of insulation that makes economic sense in your area, but in very cold climates, 9.5 in of fiberglass is not really adequate. In warmer climates, you could avoid stripping the ceiling off by blowing in fiberglass through holes in the ceiling, then patching or covering the holes. You can also apply foam through holes, but you may have to fill the whole cavity, which would be expensive overkill.
I don't think it's possible to accurately place foam through holes such that the cavity is not totally filled, but it might be worth questioning an experienced applicator. If you blow fiberglass, then you will need to add a vapor barrier somehow. Some heavy solids paints meet the vapor barrier spec of 1 perm, so could be considered to be a leaky but adequate barrier. Or you could add a thin layer of foil backed sheetrock. Or just sandwich polyethylene sheeting between layers.
Without knowing your climate or local prices, I couldn't say what the best option might be, but I hope I've given you enough ideas so you can decide on your own. Cheers.