Here's my opinion on eyelets, as I don't know of any solid study or proof on eyelets.
Eyelets, in theory, take some of the stress off the rim hole. With the bare aluminum and no eyelets, I've seen tiny stress cracks pop up around spoke holes after a couple thousand miles. This doesn't mean eyelets prevent cracking, but they sure do help.
Double eyelets are better than single eyelets, because they distribute the stress over both the inner and outer walls of the rim. But even a single eyelet is way better than none.
I think eyelets are also better for the spoke nipples, acting like a bushing. When a wheel flexes either laterally or vertically, the spokes do move a little bit, and the nipples do too. I think the nipples move better in a stainless eyelet than a rough-edged hole.
If I build a wheel without eyelets, I always use brass nipples. I have built a couple Velocity and Bontrager rims without eyelets up with aluminum nips, and they chew the nipples up and the base. I haven't seen a failure because of it, but it's a little un-nerving.
One disadvantage of eyelets is that they can pull out, leaving you with a damaged rim and possibly a busted wheel. I've never seen it happen, but I've heard of it.
