Of course there is some subjectivity in WAR. I'm not sure anyone has argued otherwise. The UZR/150 ratings are based on trained observers who rate each play made in a zone. Yes, there will be variations from observer to observer, but they are all trained and calibrated to lessen those chances. It still beats one person's personal observations of most just one team and the few opponents that team plays.
I heard the play JBJ made where he dove for that ball in left center field going away from home plate as a 40% play. Personally, it was one of the greatest catches I've ever seen. I'd say that was a 1% play at most.
It's not a perfect system, and it's not supposed to be perfect. To me, I trust the observers are faairly consistent and over a long term, it all shakes out about right. That's one reason they stress not using UZR/150 or WAR for small sample sizes, and defensive plays per game are often 0-2 for OF'ers, so a good sample size is usually 2-3 years or more.
WAR is flawed, but it does a pretty good job of assigning one number to a player that encompasses batting, fielding and running value in one.