I think the Lutece's are trapped from doing everything themselves because Booker AND Liz are needed to 'reset' the universe back to before Comstock's appearance. Without the proper motivation to do so (i.e. going through the whole narrative), it's possible that the Luteces did try direct intervention only to realize that infinite other timelines still existed with the same problems until Booker's 'choice' was erased.
In order to stop ALL of them, they needed Booker and Liz, the two people with the capability to fix the 'mistake' they'd created with Comstock (Booker as the subject and Liz to establish the paradox/get rid of all Bookers) to perform the task themselves.
I mean, if they weren't able to do anything after their 'death'/scattering, they would not have been able to give Booker the shield, which is the one thing that has a direct effect on the gameplay, while not overtly affecting the narrative except to help prevent Booker's death.
I guess I could just make an assumption that Comstock was peeping through universes and saw a more recent Booker, but that's no fun.
I believe this is what happens. Comstock looks into the tear machine later and sees the Luteces going against him to get Booker back, who had already carved the AD onto his hand. Upon seeing this, he took precautions against Booker while telling Fink to take care of the Luteces, to account for the eventuality, the same as he did when sending the security team to wait in case Liz ever showed up. (The voxophone mentions that the team had been waiting a while.)