WAR is a more ambitious adventure than BA or SLG or ERA, all of which have their own flaws and misrepresentations themsleves. Sure there is probably not much difference between a 5 WAR and a 6 WAR player. There also isn't much difference between a .240 hitter and a .280 hitter, but that difference is also viewed with equal disparity. Sportswriters even often do stories about this .240 hitter needs to be replaced with that .280 hitter, despite the difference being hits in a whopping 4% of at-bats.
And a lot of those stats where there is "only one way to calculate them," do you think that was ALWAYS the case? Batting average has so many weird conditions, you have to think a few of them were added after the first iteration of the stat. After all batting average represents "the percentage of times a batter gets a hit in a plate appearance where he does not draw a walk, get hit by a pitch, give himself up in an obvious and willing attempt to bunt a runner over, or hit a routine flyball to the outfield with a runner on third and less than two out, allowing the runner to score." You think all of that was in there the first few times someone started calculating batting average? And even then, after all that, it's still glitchy, Why is a sac fly not an at bat that counts towards BA, but it is if the runner gets thrown out at home? Did having a slow runner on third make the hitter somehow worse at the plate? Why is sac fly not an at-bats but an RBI ground out is? These flaws don't seem bother you in BA, but they do bother you in WAR.
And check out the number of changes to the SAVE stat over the years. Now THERE is a stat that has had FAR MORE than one way to calculate it. And some of them are still stupid to this day.
The only real difference is since most of us grew up with this stats, we accept them, flaws and all. And we believe that they are what they always were, because we have never known them as anything else. WAR is this whole new scary stat we didn't grow up with, and therefore it has to pass the test of being as perfect as the old ones are, even if it is still in it's infancy, and those other stats are really not as perfect as we really think they are.
There is more than one entity calculating WAR, which is why many people differentiate the two as though they were different stats. But that is really the fault of one of them unimaginatively naming the stat. No one really ever confused WARP (Wins Above Replacement Player) with VORP (Value Over Replacement Player) with WAR, despite all essentially doing the same thing, but they at least had different names. Plenty of people preferred WARP over VORP or vice versa for whatever reason, or liked some other stat entirely. And I left out slasher's personal favorite of WAA (Wins Above Average) and Bellhorn's favorite WAFL (Wins Above Felipe Lopez). OK, that last one is not published anywhere and was a joke of mine back on BDC. But all these stats tried to do the same thing.
Sure it has flaws. What doesn't? Giving credence to WAR despite that it does not always agree with what we see is like giving credence to science. Science is often viewed as fact, despite what it really is is "today's best educated guess" and any part of it can be refuted or disproved tomorrow. The same is actually true for WAR. Or WARP. Or WAA.
But not WAFL, which was perfect.
Until Felipe retired.