The horizontal pipe becomes a lengthened trap. A great deal of material in the extended trap will make additional resistance that can make it more difficult to move a lot of solids.
If the horizontal pipe leading from the trap curve is not at least level (a slight slope to the wall is a bit better to help the pipe not act as a shelf to leave soiled water resting on the pipe) this is not usually the cause of having to run the disposal every time to act as a pump to force the water down.
The venting system behind the wall should permit water to spill freely over the end of that pipe into the sewage system. I would have the installation examined by a person qualified to judge if your installation is at least to code and make suggestions to improve the situation.
Have a Licensed Master Plumber (LMP) look at it, not just some Loud Mouth Person.