Loop vents, for use where direct vents aren't feasible (such as in kitchen island cabinets), are typically drawn, built, and described as comprising three elbow fittings--two 45-degree elbows and one 90. This results in a peaked shape that approximates a single U-bend.
What's the importance of this shape, and why are they not simply built with two 90-degree elbows and a squared top, or two 90s joined in a U?
From the International Association of Plumbing and Mechanical Officials (IAPMO) "Uniform Codes Spotlight" archive from February 2018:
The configuration of the return bend using 45 degree and 90 degree elbows purposes to maintain a vertical angle (see Section 224.0, Vertical Pipe). This is to protect the return bend from accumulating waste and to prevent waste from flowing down the return side of the bend if a blockage occurs.
There is no reason you need the three sections vs one 180 degree return piece other than you have copied in one of the oldest and most used plumbing pictures on the internet.
I do my own plumbing and hire out plumbing for some jobs. I would only expect to see the 3-piece 180 turn (which is really 5 pieces) done by a hack - seriously. A good plumber does things in an efficient manner and knows the more pieces added the more chance for error - imagine an electrician putting 4 junction boxes on a circuit (by code) when he could have used 1 or none. Same thing here.
Why was this done? Probably because 20-25 years ago it was hard to find specialty pieces like a wide 180 return or a taller one. I am guessing that using the standard 45-90-45 available at most stores - that this gave you the correct minimum dimensions.
Now you can get these 180s in a variety of sizes - even big box carries 2-3 sizes by default at the stores. At plumbing wholesalers you can get these in 15-20 sizes so you can now in fact mimic this tall/wide 180 return with one piece.
Do I agree with the need for a size this large? No. I have also never had an inspector say one word about using a basic 180 return for a vent (these are the same size as your basic "trap"). You can get the same basic premise and functionality by extending the straight PVC out of the top of your sanitary tee by a couple more inches. Also the smaller 180 is more practical as these are huge plumbing pieces and we don't have unlimited room to do whatever.
The return bend used under the drainboard shall be a one piece fitting or an assembly of a 45 degree (0.79 rad), a 90 degree (1.57 rad), and a 45 degree (0.79 rad) elbow in the order named. Pipe sizing shall be as elsewhere required in this code.
