For that to happen you'd have to change the reward system.
Rewards dictate the player behaviour. As long as the rewards are based on amount of fights (ie, losing a sector generates more rewards) then there won't be proper war. The rewards would have to be in gaining and then retaining sectors. Only then will Guilds have to fight each other for the space.
However, early on the biggest Guilds worked out it's cheaper on the treasury to ignore their biggest opponent if that opponent does the same (unspoken mutual respect) and only focus on the smaller Guilds.
Even if the rewards system changes, you'd still have the problem of the opponent understanding that it's cheaper to ignore the strongest Guild on the field if it's reciprocated. That amplifies any power dynamic problems between Guild strengths, one that (ironically) farming was partially alleviating once it got to involving more partners into the checkerboard.
So if you really want war, you'd need to make sure each tier of strength has a equal to fight against, and that they're actually fighting each other not teaming up against all the weak Guilds.
Strategy wise it makes the most sense for the strongest Guilds to team up as then no one can stop them. Fun wise it's detrimental to any games health when that happens
Even if you changed it so only #1 got rewards, that on its own wouldn't fix the problem as #1 and #2 could still team up and swap each season which one of them wins. (Not to mention that'd likely make everyone else quit playing anyway)
I've been gaming for a while and I've seen this happen before. For instance in the early days of WoW BGs were fun, but at the very top you had politicking about the personal ranking spots from 1 to 10 on a weekly basis. Because those rankings were so important you had elite groups that farmed 24/7 and ruined the game for the casual player. This did not have a solution because the populations on individual servers dropped and there wasn't much competition.
We're in the same situation - 3-4 strong guilds per server, 5-10 minion guilds that have been trained to follow basic instructions, but wouldn't be able to enforce a checkerboard without a strong guild, and the rest are casual.
Years later they came up with a solution in WoW - cross-server battlegrounds. That wasn't great either.. you had elites farming the casuals but from different servers. So this alone wouldn't work here because what's to stop someone from making another town on the other server and coordinating with a strong guild on that side
When matchmaking rating was introduced things got a little better. We kinda have that here but it's not working because you need way more stronger guilds to balance things out.
It will be hell from an engineering standpoint, but here's the solution:
Introduce X-server BGs
Add an elite division above diamond with a set number of guilds. The number can't be too big because you don't want regular diamond guilds randomly getting in there, the top guilds should be fighting to get in.
Add GBG specific ranking for each server and revamp the current MMR system - it can't have a cap of 1000 because you can't tell who's actually #1, 2, 3, 4 etc
Honestly you could livestream it if you could get the #1 guild from 8 servers on the same map.
Of course cooperation would still be possible, but at least they'd be doing it to each other and not to the small guilds.
...and of course limiting the number of attacks per day by introducing attrition and having people display their individual strength and strategy is the much simpler solution, but what do I know, I've only been gaming for 25 years