Wins above replacement would make a terrible daily stat.
For one thing, there are all sorts of margins of error in the calculations -- around park factors, baserunning opportunities, value of positional adjustments and defensive ratings -- that mean relatively little in a season, but could really tilt a single day. But for another, WAR is all about taking a very complex range of data and turning it into something simple. A single game, though, already is simple. WAR would arguably make it unsimple.
And so, WAR is not a daily stat. Nobody publishes it or talks about it, and you can't go back and look at what Babe Ruth was "worth" on July 3, 1923.