the debate between mil and moa will probably go on for years. But since the original question was why the love for moa, then here's the best example i can think of for my personal reasons. I am sure some others can relate this to their style of hunting.
As i wrote earlier, i started using reticles to range before we had rangefinders that would reach out to beyond 300 yds on game animals. I used those same reticles for holdover, because there weren't many affordable scopes that had accurate click adjustments either......4 minutes on the dial would move the poi 6 minutes type of thing. Takes me a long time to trust a scopes adjustments and repeatability.
My first rangefinder was the bushnell 400.....sure, it would range 400 on a stop sign or a shiny pickup truck, but try to get a range on a coyote that's 300+ yds away! Ha! Even the 800 yd model that came next wouldn't range a coyote much past 400 yds! Yes, todays rangefinders are much better and needless to say, much more precise than reticle ranging...........as long as we've got time and the right scenario to use it.
Calling coyotes is not about "long range shooting", but sometimes we have to take a long shot. Here's the example i am getting at.
Said coyotes are coming in to the call. We're all camo'd up and hiding in the shade. We're sitting on our butts (in order to see over the sagebrush) and the rifles are resting on cross sticks. The pair of dogs are doing the usual, they're coming in toward our downwind side. By time we see them, we realize that they are just about to get our scent and leave the country pdq.
First thing we have to do is get them to stop long enough to get on them with the rifle, and fire before they decide to get downwind any further.
Do we have time to pull the rangefinder out of our pocket and get an exact range? No.
Do we then have even more time (and additional movement) to look down at the butt of the gun to see how many minutes or mils we gotta dial? No.
Do we have the time (and even more movement) to reach up and dial the dope? No............by time we do all that stuff, the dogs are moving again and we've lost our shot.
Same situation if we call in and shoot 1 coyote but the other takes off running. We're sometimes able to get the 2nd one to stop for a shot, but they don't usually stop for long. Darn sure not long enough to go through all the above range - look - and - dial steps.
Now here finally is where the moa (quickly and crudely reverted to iphy) comes in. First off, i'd memorized my holdover amounts out to 500 yds. Secondly, i'd previously visuallized and memorized the image of a coyote against the reticle. I knew that a 9" coyote would cover 3 "minutes" in the scope at 300 yds, 2.5 minutes at 350 yds, 2 1/4 minutes at 400 yds, ect.
Crude, yes. Exact, no. But it gets me close enough to put the bullet in the boiler the majority of the time out to 400 yds in a rush and 500 if i can take my time and think/prepare/steady a little.
Can the same thing be done with a mil reticle.? Yes, but every increment i mentioned is less than 1 mil, so now we're trying to break down the spacing to 1/10's to even get close to the same precision as using 1/4 minutes. And again, we're doing this in a hurry with coyote fever making our nerves a wreck.
Medium range hunting is often not about absolute precise range, it is often about how quick can we put the bullet in the vitals from a less than ideal position. I've lost count as a hunting guide that i've whitnessed people take too much time trying to range and dial for a simple 300 yd shot. It's too much movement and just gives the animal enough information to get them nervous. Especially antelope it seems. Take that time instead to get steady and focus on making the shot, calming the nerves, get the breathing under control, ect. The buck in my signature didn't give me time to even think about dialing a knob. It was hurry up, go prone, lead by two body lengths and squeeze.
When a coyote is between 300 and 400 yds; "close enough" on the range will mean the difference between a dog down and one that got away. I want "close enough" to be quick and intuitive, iphy is the quickest way i know of (for my brain anyway).