Any reason not to use Tyvek to cover exposed insulation

According to the Material Safety Data Sheet (MSDS) for TRYMER(TM) 3000 Rigid Polyisocyanurate Insulation, there should be no problems (for this specific product anyway).

I also found the MSDS of an example Expanded Polystyrene Board, which does mentions off-gas issues. Though it only applies to large amounts of "fresh" polystyrene, being stored in a "confined, unventilated area".

fresh polystyrene contains residual pentane and if large amounts of EPS materials are stored in a confined, unventilated area such as a semi-trailer truck, pentane may off-gas and create measurable airborne concentrations.

If you know the specific product you'd like to use, it shouldn't be that difficult to find the MSDS for it on the internet.

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...)