Characters on the same account cannot mail eachother.
Also, having the same account shared box option is highly preferable over an improves mailing system.
1# It is like a battle box where we can keep all our best comps
2# Mailing system improvement would charge us 1k each time we wanted to get a pokemon from another character on the same account, and its a much slower and more tedious process than simply being able to access a box with them all already there.
#3 People have been wishing for this Battle Box feature for years. Its all Pros and no Cons and helps us keep scammers from robbing us as we are currently forced to either trust someone to hold our pokemon while we get on our alts, or make entire alt accounts to mail them to.