Many years ago during our B737 endorsement with a Boeing instructor pilot, we were told that the purpose of immediate manual speed brakes (rather than count on the reverse thrust lever action to raise them), was to dump lift as well as create drag at high speed. He went on to say that the reverse thrust lever was a back-up in case the crew forgot to pull manual speed-brake. This instructor would go off his trolley if you forgot to raise the speed brakes manually on an abort.
He briefed us that Boeing never envisaged use of the reverse thrust levers alone as the prime means of raising the speed brakes in an abort. In any case it may be unhealthy to reverse an engine that is on fire if the abort was due to a fire warning. Thus if your company requires the use of reverse thrust lever actuation as the primary means of getting the speed brakes up, it is worth thinking about the engine fire case.
During simulator sessions we were shown an abort at high speed using max reverse thrust only. The purpose of this demonstration was to show the excellent initial retardation of reverse thrust and as the speed reduced below 100 knots the retardation was less and less until at 60 knots the aircraft kept on coasting down the runway and off the end while still making lots of noise at full reverse. We then saw an abort using maximum brake and speedbrake and the difference was phenomenal. All this on a dry runway. It is on a wet runway that reverse starts to come in on its own as the brakes don't get a good grip initially.
What we often see in the simulator is the pilot frantically attempting to haul through the interlocks into full reverse on an engine failure abort and failing to concentrate instead on maintaining maximum braking (if he has overridden the RTO function - which people sometimes do inadvertently while using rudder to keep straight on a single engine high speed abort).
As someone mentioned earlier, on a dry runway by the time you wind up into full reverse on the live engine, the brakes have done their job and the speed is down into the reverse useless range.
There are companies that have the PNF sharing the abort actions by being responsible for reverse thrust actuation and modulation of reverse. This might work well in a simulator where you know that aborts are bound to be practiced. In real life, however, I venture to argue that this is a recipe for confusion. Especially if the aircraft started to weather-cock off centre line requiring judicious reverse handling. A case of who's up who, and who is paying the rent!
A high speed abort may hopefully never happen in one's career but if it does it may well be the most critical instant decision that one ever has to make. I would also venture to say that during certification flight testing the test pilot personally takes all the required abort actions - I am sure he would not pass the responsibility of reverse handling during the abort to the co-pilot? In my book anyway, the abort is a one man handling operation with the other pilot monitoring.