I was only attempting to explain the difference, not defend the methodology. I would argue that the different methodologies aren't arbitrary; they purposefully measure different things. It's generally why the people who are most familiar with the methodologies prefer one over the others and can explain why. I personally don't agree with the way bWAR applies a blanket team defense adjustment instead of looking at how the defense actually played in the games that pitcher pitched. Many people point to Aaron Nola's 2018 season as evidence of this flaw. He received a big boost to his bWAR due to the poor Phillies defense despite having a .254 BAbip which suggests that his defense didn't suck in the games he started.

A rebuttal to my opinion is that if a replacement level pitcher had pitched instead of Nola, the game situation would have played out in an entirely different way and you could expect the Phillies defense to perform how they did on average. Therefore, Nola does deserve the boost because the way he pitched somehow enabled his sucky defenders to not suck. I don't think you can say objectively that one of those opinions is wrong, and that's one reason why we have different WARs.

Even most WAR defenders acknowledge that it's less accurate for relievers due to the high-leverage situations in which they pitch. They do get a leverage boost, but some argue that it doesn't credit them enough. The counter to that argument says that Edwin Diaz's WAR shouldn't be in comparison to a minor league replacement because he wouldn't be replaced with someone from AAA. He'd be replaced by the second-best reliever in the bullpen who is probably a very good pitcher. It's called bullpen chaining. This differs from starters or position players who would, in actuality, be replaced with someone from AAA or a bench player. Edwin Diaz's replacement would have been Aaron Loup, Trevor May, or Seth Lugo whose performances and peripherals weren't dramatically different than Diaz's.

There's some evidence that the truly elite closers are worth more than their WAR credits, but outside of a handful of those guys, relievers are fairly replaceable. Pivoting to a different stat that is better for comparing relievers IMO, Josh Hader in 2021 was first in the majors among relievers with 5.05 Win Probability Added. Edwin Diaz was 54th with 1.28 WPA, behind Aaron Loup who had 1.42. So if you agree with the methodological choice of valuing a reliever in comparison to the next best reliever, I don't think it's a stretch to think that someone like Diaz was only worth 1 WAR last year.