"The trench contained ion engines, hyperdrives, and hangar bays". – Valorum
"In the briefing Dodonna says, 'You're required to maneuver down the trench to this point.' " – Todd Wilcox
Just as the trench is protecting the hanger bays from the sun, it protects sensitive equipment that is required to protrude from the surface from errant mishaps, by simply employing a giant trench to recess them into.
Which in order to assault and have the correct angle to fire upon anything in the trench, you must make yourself an obvious target flying a given trajectory. It's like a camel's eyes in a sandstorm.
"The trench was probably actually built to recess the thermal exhaust port and other items from the surface. Note that it was very difficult to attack the port since it was in the trench." – Todd Wilcox
Aye, changing course, Commander... Issue the alert: SPF 5000.
Note that the equatorial trench isn't the only one.
Several polar trenches are shown in the rebel schematic animation. They radiate out from somewhere near the pole to approximately halfway towards the equator. –theforce.net
This is all for the most part, speculative. But having more than just the one trench suggests that they have some use, whatever it may be, other than being a flat-out "battleground written in to the story."
To tie this into Lucas' inspiration, in aviation it's hard to account for drift, so you plot your course along any natural landmarks you can find. Ideally, like a river leading up to a dam, or in this case a trench. Which when followed takes you exactly where you need to be and keeps you on course for your target.
Conventional weapons require the proper trajectory when launched. Which makes you, in essence, a sitting duck because that's where they're going to have put the guns:
The plant is in a seemingly impregnable location beneath an overhanging cliff at the end of a long, narrow fjord lined with numerous anti-aircraft guns. –633 Squadron
Vader flippantly decides that he has to go out there and save the day, all the while the batteries in the trench were doing their job just fine. (Way to go, you burnt-bacon smelling Nurf herder.)
Equatorial and polar trenches are installed early in a Death Star's construction because, not only do they house vital equipment, but they also make for the 'spine' of the superstructure, onto which everything else added.
The first thing you need for any project is a place to warehouse delivered supplies and docks to receive personnel. The first steps in construction (planetside) are the foundation and the framing. In space, they're one and the same: a superstructure.
It is also possible that the 'trench' is simply an artifact left over from construction, but was designed to be put to good use afterwards. The giant 'U' shaped band around the DS might have been required to be oversized, to support itself and the subsequent addition of sections, until completion.
