I know you weren't making any arguments here, but I believe one thing should definitely be clarified. When we say "average is 2 WAR", are we talking about the mean or the median? Because I think a distinction is important.
When you're talking about baseball, where such a large amount of the total WAR per season is contributed by the game's elite, the "average player" (the median) is almost always more valuable than the "average WAR" (the mean). Said in another way, even if the average or mean WAR is 2, a 2 WAR player is actually quite a bit above average (he is above the median; he is better than more players than he is worse than).
Examples from 2016:
1 or more Plate Appearances
- 971 Players, 569.5 WAR
- Mean: 0.6 WAR
- Median: 0.0 WAR (Justin Morneau)
50 or more Plate Appearances
- 542 Players, 585.9 WAR
- Mean: 1.1 WAR
- Median: 0.6 WAR (TJ Rivera)
100 or more Plate Appearances
- 438 Players, 592.1 WAR
- Mean: 1.4 WAR
- Median: 0.9 WAR (Hyun Soo Kim)
300 or more Plate Appearances
- 268 Players, 562 WAR
- Mean: 2.1 WAR
- Median: 1.7 WAR (Giancarlo Stanton)
Qualified:
- 146 Players, 433.9 WAR
- Mean: 3.0 WAR
- Median: 2.6 WAR (Hanley Ramirez)
In baseball, if you have a player on your roster who is contributing the same amount as the mean WAR under any set of criteria, he is by default an above average player. That is, as long as by "above average" you mean "better than half of his peers".
TLDR: A 2 WAR player is actually above average, even if the "average WAR" throughout the league is 2. Russell Martin (1.9 WAR) was an above average player in 2016.
Note: Sorry for the semantic satiation. Not actually sorry. Average. Average average. Avg. Average batting average. Above average average average. Every edge's edgy average.