I think they asked Junichi about this. I remember someone replying, The E4 remained behind to protect the region while the Leaders and Champions were away.
That is mostlikely the reason, It would be quite easy for evil organizations to take over a reign with all strong trainers in Unova and it acctually makes sense
but although theres gotta be someone who protects the region I think it would make more sense if the Gym leaders did that since they are in multiple locations, 4 people in maybe 10 cities per region is still hard to protect.
And the E4 are the 4 strongest trainers of a region it makes no sense for them not competing in the PWT while the Gym Leaders are
I think it is much more reasonable if a gym leader stays in his/her position as without badges you can't enter the E4 what if the adventure of a new trainer starts while the PWT is on. he would be screwed from the start because there are no Gym leaders. Only trainer with 8 badges in a reign are being able to do something for the time that the PWT is on.