Yes, it seems that water would be directed to the center of the pile quite effectively with that shape (both from precip and from irrigation), but it would also dry out more quickly because of the increased surface area compared with a simple mound. It seems that a simple mound also benefits from the thick layer of material at the center, which retains moisture.

I strongly believe in covered compost piles for arid climates, and have had years of success by simply surrounding the pile with straw bales, and then covering the whole thing with a sheet of plywood. I build a small hinged trapdoor into the plywood for easy access, and pull off the entire top anytime I need to mix or harvest the compost (both of which I do only a few times per year). We average 13 inches annual precip with very little humidity where I live.

A less formal version of this is simply a compost pile that is constructed all at once (not added to periodically like the typical kitchen compost described above), watered, then covered with a thick layer of mulch and left to decompose.

Maybe the question is really one of water delivery versus water retention. Certainly an open pile in bright sunlight can work fine in an arid climate as long as it is watered frequently. I prefer to create an environment in which the moisture of the original compost material is retained, rather than worry about how effectively water can be put in. I do occasionally pull off the top of my compost pile during a rainy spell, or even throw on a bucket of water if the pile seems too dry. Of course if the starting material is very dry (such as old yard waste instead of nice slimy kitchen scraps) you would need to pay more attention to this.

Anyway, good luck with your composting...

I saw a site online where this guy in the arid hot part of India , he covered it with red clay after he had formed his pile, and that held in the heat and the moisture. They would break it apart, turn it. and then cover it back up again with the clay.

I have two closed compost bins and a large open pile in a free-standing wire dog kennel. If I don't water the compost frequently, it is slow to break down. In summer I water the compost at least four times a week. In winter, I water the compost about once a week (unless it has been raining or snowing). Chopping up vines and larger items to twelve inches, or less, helps the materials to decompose more quickly.

I have a slightly dished compost heap, because the center decomposes faster.

We don't get enough rain to "collect" ... but it does hold dirt for tomatoes.