Using PA as a barometer invites extreme survivor bias. You're doing weird stuff that doesn't make sense and isn't necessary.
A league average (100 wRC+) hitter with neutral defensive value and neutral baserunning value is worth 2 wins in a full season.
To understand WHY you need to know how WAR is calculated. The components of WAR are:
Hitting runs
Baserunning runs
Fielding runs
Positional adjustment
League adjustment
Replacement level adjustment
The first three components are all runs relative to league average skill at those specific things.
If a player moves through the first five components and has calculated exactly zero runs, but they played a full season, then they get 20 replacement level runs. A league average player is worth 2 wins.
But why? Because it's WINS ABOVE REPLACEMENT and we specifically want league average players to be given an arbitrary number higher than zero. The 2.0 = average line was set in the creation of the statistic!
But why 2? Because there is a set number of wins in baseball, and we know that an average team (.500 win rate) playing at true talent has, on average, a set of average players. We can crunch the numbers and figure out how many wins an average dude is worth on this scale.
We could just as easily use WINS RELATIVE TO REPLACEMENT and the league average player would be worth zero wins. But, WRR is an inferior acronym.