Over-using robots and multiball does prevent you from developing the ability to perceive where the ball is going by watching the opponents bat. You can always do a drill with a coach of training partner to develop it though. Slow (but deep), random balls where you try to win the point through deception instead of power.
I cannot see how reaction time can be the issue. Human variability here so so small that it shouldn't matter.
Also running to the BH to do a FH is really old school. It better be a kill shot, because if it isn't and your opponent just blocks it back cross court with decent placement, you will be in trouble. It's better to use BH from BH. Falkenberg is really outdated as it includes BH from FH. A lot of coaches just teach what they were taught 30 years ago and don't update their skill-set / knowledge for the modern game. It's almost impossible to play that old-school style anymore as players stand closer to the table, and the ball comes back really quickly.
If you have problems with high balls to the BH, you are probably playing too far away from the table and taking the ball too late. You need to get the ball right off the bounce. Otherwise your only option is to take it late even further away from the table - but this will leave you at a disadvantage, do I don't recommend it.