If you take a program and replace, skip, change reps/weights on an exercise in that program, it is (unless stated that said modification is okay) no longer the same program. Whoever wrote the program picked and planned things for specific reasons, and a big not insignificant part of a program’s success is the lifter’s belief/trust that the program is effective. Trust that the things in the program are there for a reason and execute it to the best of your abilities.
On a more technical note, building strength in a reduced/stronger range of motion can definitely have carry-over in weaker positions of the main movement. So yes floor presses could still be a good movement for building bench even if you typically miss off the chest. Also, a good program will balance weekly load efficiently. In the bench, shoulders are most taxed and vulnerable at the bottom of the movement, so doing more at-the-chest work might just overwork this area and lead to injury. Reduced ROM movements like floor presses can be a great way to get more pressing volume in without adding to potentially detrimental volume to the shoulders.
As you mentioned, if your issue with missing off the chest is technical, I would recommend being more diligent about your setup and technique when performing the competition movement. Getting stronger where your technique breaks down is a poor substitute for fixing your technique.