5800-2300 is a slight difference in the context of a high-pop realm. Just check the other high pops on the same site, non-rp high pops have something like 8000-500 and ultra high pops go as far as 11 000-400.
I have a couple horde characters on AD, last week I got bored and popped on to there and decided to try out War Mode to spice up doing dailies. The amount of Alliance characters I encountered could be counted on my fingers and toes and quite literally none of them was interested in fighting me. At one point I had tagged a rare and there were three Alliance characters just watching me on flying mounts without interfering. Honestly felt like they were afraid to approach. The closest I got to getting attacked was when a rogue on a flying mount targetted me, stopped for a couple seconds to think about it and then went on his way.
The one time I actually initiated a fight on one of them, the dude was so helpless it was actually sad. I never seen anyone trying to backpedal so hard in my life. Decided to not attack anyone else because it felt like bullying.
And no, it’s not like I’m some l33t pvper or can crush everyone because I have sick gear. I only do PvP to cap conquest and the character in question is 430.
Not sure why we are getting so different results. Maybe you are trying to do WM during peak hours on Wednesday and the weekend? Maybe there’s Alliance death squads from other realms sharding on to AD during those hours? Dunno.