I am rather curious what the War Mode population would be without the current rewards and benefits, as I have a sneaking suspicion that you'd see a huge drop in participation (especially from Alliance). However, the resulting population isn't necessarily the goal of War Mode, as I believe the goal was to remove being locked into PvE/PvP servers by offering a choice. But if Blizz was highly concerned about participation being so low or lop-sided that they needed to add a carrot, I think PvP-oriented rewards would've been better than XP/gold/AP gains... because as it has already been stated, you feel the need to have War Mode on else your holding yourself and/or your guild/raid back by being slow. Despite that "need," you technically don't have to benefit from those at all, we just convince ourselves that we do.
Be that as it may, there's much larger issues at play when it comes to the intermingling of reward systems, and the consequences of such have trickled over into War Mode. I think the proposed Shadowland's change of the weekly cache rewards being tied to all PvE/PvP activities instead of being separated will go a long way towards encouraging people to participate in multiple facets of the game. Now, I hope Blizz avoids the pitfall of making players feel like they need to do all content in order to avoid terribly weekly loot. If anything, an 'either/or' system would likely work best, as in you can pick a PvE or PvP content, and instead of needing to do both to maximize your loot level/chances, you just need to do one activity of a certain difficulty.
A common complaint I've seen is that M+ people tend to loathe having to do rated PvP to get a second loot chest in BfA, and rated PvP people loathe having to do M+ to also get a second loot chest. I think the issue is the same mentality as the War Mode reward system: Blizz is trying to entice you do try something different, but in the end most people feel like they're forced into doing it. I think it'd be much better to have doing a M+ 15 give you the same benefit as getting 2.4k rated, but you only need to do one as you don't get more power rewards for doing both. I know I personally used to like some aspects of PvP, but I got burnt out because it felt like a chore on top of all the PvE content I was doing because I "needed" to do PvP content to help with PvE.
If anything, I think I'd support War Mode just being a toggle for PvP and that's it. If there are rewards, have it be for PvP-oriented content and rewards only. I'm not exactly sure how one could prevent extra power/progression gains needed for PvE to not be available in War Mode with an extra reward system, but I guess worst case you could just have unique War Mode transmog or items that can't work in instanced PvE. As a slight aside, I've always wanted a PvP reward system that was solely based on outdoor content versus instanced PvP content.