Roof Trim Trainwreck

I thought this piece of wood was some kind of trim, but now I think it was only used to wrap the asphalt roofing around to create a crude 'drip edge'. I'd like to research when galvanized drip edge was invented because this method is the most half-assed I could imagine. This is how you build a dog house. The water still runs under the asphalt paper and onto the house. It doesn't drip off.

it's hard to see but the red painted asphalt roofing is curled around that piece of 1.5'' wood and nailed in place, like it's a crude loop in the paper intended to create a seal of the underside of the roof. but curling asphalt paper this much causes it to decay at the edge very quickly. It lasts a year or two but then it cracks at the top bend and then it acts as a gutter directing rain runoff into the very place it was intended to protect.

For $8 a homeowner can buy a 10 ft length of 4''x4'' galvanized drip edge, like I used on my garage. On the rake you install it under the asphalt roof and over the tar paper then nail it down. or whatever you prefer. Rain runs onto the drip edge and then kicks off the house. The drip edge never cracks, rusts in like 40 years and can be reused. A roof this small would cost under $100 to completely surround with 4''x 4'' galvanized drip edge. Or you could be really cheap and get 1.5'' x 1.5'' drip edge and do it all for $50. Why would someone save $50 or $100 and compromise the entire roof deck by creating a doomed drip edge with crappy asphalt roofing? It's a rental, is the answer.

As near as I can see this top layer (of three layers) of rolled asphalt mineral coated roof is not more than 5 years old, but they used no asphalt sealant at the laps and seams (that one black line in the mid ground is a post-install crack repair using plastic patch). A gallon costs $19, so I'm hoping they had a good time with that huge savings. The material itself doesn't leak but the wind blows the seams around. The only leaks are at the eave and corners where water rolls back under the loose roofing and down the old stucco and into cracks or behind window trim. The roof material isn't the problem.

What bothers me is that the method of curling hot asphalt roofing in a circle around a piece of wood and nailing it to the side of the house sounds way more complicated and time consuming and difficult that simply running the roofing to a pre-installed galvanized drip edge is, and then nailing or adhering the paper to the drip edge. I don't see how this method was faster or cheaper.

This is what 4'' x 4'' drip edge looks like after Oggy nailed it to the eave side of the garage.

Note the professional overlap of two different drip edge sizes. Also, note the insane low slope arch that forms the pitch of this odd roof. I figured,  rain can't run off the rake unless it is blow by wind so it only needs a 1.5'' drip edge. Furthermore, the whole thing is an off grid shed...that I plan to demolish eventually.