I mean all else equal, the weapon specialist will just be a better shot, because of his characteristic bonus.  Also, due to his aptitudes, he's just going to contiue becoming a better shot than the stormtrooper, due to the exp curve.

I mean, on the table top game, the stormtrooper has a much better BS than the guardsman.  In fact, the stormtrooper has the shooting capability of a space marine!  What the stormtrooper is NOT as good as the space marine in, what the stormtrooper is equal  to guardsmen at, is WS!  And in Only War, the stormtrooper is suddenly a WS powerhouse, thanks to his aptitude!  What's up with that?

I feel like this system is conflicting quite a bit with the empyrical evidence already put in play, already observed by the players, in the table top game.

The Storm Trooper does not have the Weapon SKill Aptitude.  The Storm Trooper has been modified throughout the playtest period.  If you will check Beta Update 7 it will have the list of the changes needed for the downloaded Beta.  Even then the final release might have further changes.  The Storm Trooper now has the Finesse Aptitude instead of the Weapon Skill Aptitude.

Also the Weapon Specialist is more like the table top IG veterans.

Have you not looked at the various Updates?

The Storm Trooper is no longer a WS monster. His job is to have better gear than everyone else and to lead the squad with his experience.  If you want him to have better BS, buy it.