Does the captain always control thrust on takeoff?
I believe your referenced material is mixing up "Captain" with "Pilot Flying". The person in control of the aircraft should have their hands on the throttle, Captain or not.


  If the take-off needs to be aborted, can't the captain just command the FO to "abort" or take control by saying "I have control" or similar?


Having your hands on the throttles has a number of advantages:


You don't have to waste seconds (which at 200mph means about 300 feet per second)
You don't have any confusion (i.e. "What did you say?")
You don't need to discuss it with the other person (you say abort, FO says OK)


A lot of companies require both the PF and PNF's hands to be on the throttle at the same time, which has the advantages of 1) assuring that the throttle is set to its maximum power, and 2) either one can abort without having to command the other to do it. Either pilot (or the FE if they exist) have the ability to call an abort before V1, and the entire cockpit crew should follow that course without discussion until clear.


  I also recall seeing videos of the flight engineer pushing the throttles.


There are also cases where if a FE is required (which usually is not the case anymore), that the FE also has their hands on the throttles along with the pilot/copilot. 


  Finally, will pulling back the throttles be enough to abort takeoff safely without braking? Surely it would just cause more problems?


Depending on how fast you are going, it is almost always the case that you will have to brake as well. Airplanes are pretty slick at rolling down the runway and relying on drag alone to stop you will probably result in an overrun. Usually the PF will be the one on the brakes, but the PNF may also be applying pressure just in case.