kalabdel, cumulative error is most often a problem when your system involves tensioning a web, as in a paper sheet, plastic sheet, or even a metal sheet. For example, if the error, however miniscule, is always negative, that would eventually accumulate enough for the sheet tension to go slack. On the other hand, if it were always positive, the tension would gradually increase until a sheet break or roll slippage would occur.
The benefit of an encoder speed feedback system, usually called "closed loop" is that, if a pulse or more is missing on one revolution, it will be made up on the next revolution. That way, the error always sums to zero over time due to both positive and negative error swings.
Cumulative error also can be a problem when you are trying to coordinate the position of one part of a process to another part. For example, if you are trying to imprint something on a paper sheet that already has printing on it, it is essential that the new impression be made in the same place on the sheet image. Cumulative error would permit the added impression to slowly "walk off" the sheet image. Clearly not acceptable!