The problem with WAR is that people like it. It allows them to do things that are otherwise difficult to do. Like comparing players that play different positions. Or even comparing the value a pitcher brings to a team with the that of a position player.
The issue with this is that WAR is a subjective stat. It is taking stats that someone thinks are important, weighing them to emphasize the most important, and then combining them and putting them on a scale. Assuming the math is legimate, we are when using WAR, agreeing that the author used the correct stats, and weighed them the way we individuals would if we were comparing two or more players. That is nonsense of course. Not everybody on this site would agree on something as simple whether ob% or slugging % is more important for example , much less what stats we should use or which are most important.
WAR is largely a lazy way to compare players. Since it is subjective, it is not WRONG, merely an opinion about how players compare.
Many of the new stats like FIP and most defensive stats, are like that. They are subjective stats that give you an opinion about what value players bring to their teams.
Every single method of baseball player evaluation since the dawn of time has been subjective. That's not unique to "new stats".