Largely, because of how sports statistics were created.
For a long time, statistics tended to be results oriented. Football statistics came from play by play, which went something like (below is my approximation, not actual PBP):
SF 20, 1st and 10: Incomplete Pass to 84 Rice
SF 20, 2nd and 10: Pass to 84 Rice 18 yards to SF 38
SF 38, 1st and 10: Craig, 5 yards to SF 43
Etc.; it gave basic information, but not the detailed information you have now. You can see an example of this on Pro-Football-Reference's PBP of the 1989 Superbowl.
As such, you can't separate things like run-after-catch and things like that from the total play; you simply get a single number.
With the advent of advanced statistics, you get interest in having that additional detail - as you say, passing yards with little run after catch are very different from ones with more run after catch.
In the interest of keeping things comparable from one era to the other, "old" stats will tend to stay the same: QB Passing Yards will still be total yards, for example. But instead, you have new statistics.
- ANY/A: Adjusted net yards per attempt. This doesn't remove YAC, but does adjust passing yards in various ways (penalizing for INTs, bonus for TDs, penalize for attempts and sacks).
- DYAR: Football Outsiders has two statistics, this one being closer to passing yards. DYAR does not take YAC into account, but takes into account things like position on field and yards to go, and makes defense adjustments.
- QBR: ESPN came out with QBR, which is the only major stat I've seen that does adjust QBs down for YAC yards.
Advanced statistics often try to strike a balance between simplicity and descriptive power, which is likely why ANY/A doesn't include YAC adjustments. Additionally, any statistic that is not determinable from play by play will not be possible to get for older games, and may be difficult to get for games before it was created; Football Outsiders' Game Charting Project for example requires multiple volunteers watching game footage of every game ever played, have been for several years now, and are only to about 1989 currently.