It definitely depends on what you're trying to do with it. WAR is not the best at explaining historic team-level outcomes; that's what actual wins and loses are for. But if we're looking forward, the "distributional luck" piece isn't predictable. You don't plan for having a great record in 1-run games or having a disproportionate amount of clutch performance. You build a team with the highest baseline level of ability to produce and prevent runs. And we don't have a better way of assessing that than WAR, broadly speaking.
If your bar for whether a not a stat should be mainstream is whether or not it tells "the whole story", then we shouldn't look at any stats ever. But if you're trying get a handle on how "good" your team is and whether or not it's likely to be competitive, WAR is the best framework we have for doing that. As a starting point, at minimum, and likely still quite a bit better than whatever ad hoc process you'd attempt to put together absent WAR.