The explanation I have always been given for long, curled peyoth among those that have the minhag, is that it is for beautifying the misswah of peyoth. However, there are seven peyoth, only two of which are the sideburns.
There are the peyoth of the head, which are beautified.
One is liable for each corner. Therefore, a person who shaves both his temples - even if he were to do so simultaneously and had received only a single warning – is [liable for] two measures of lashes. Rambam Hil. A"Z 12:1
But there are also five peyoth on the beard which are not.
The beard has five "corners": the upper and lower cheek on both the right and left sides, and the hair on the chin. One is [liable for] lashes for the removal of each "corner." A person who removes them all at the same time is [liable for] five measures of lashes. Rambam Hil. A"Z 12:7
Given all the peyoth are misswoth, why do only the peyoth of the head deserve beautification? Why not the peyoth of the beard?