A 13 year old should do their own laundry.
13 year olds are fully capable of doing their own laundry and it can teach them a valuable life skill they'll need when they reach adulthood.
It's okay to do the laundry for your 13 year old or any kids you have but it's also good to have your kids do their own laundry when possible as well as it also saves you work.
Most children by age 13 have the physical skills and cognitive skills to safely operate a washing machine and dryer.
Even my 3 year old son helps put laundry in the washing machine and helps to start it with my supervision and he also helps put laundry in the dryer and starts it with help.
My 7 year old son does his own laundry and knows how to operate the washing machine and dryer and does a good job and he loves it.
Some kids learn to do laundry early than others by most kids start to learn to do their own laundry by age 8 to 10 years old.
By age 8 to 10 kids can also start learning the basics on sorting clothes by color and also understanding fabric care labels and using the washing machine with supervision.
It's not mean to make your kids do laundry or chores as it teaches them important life skills that they will require when they reach adulthood and get out on their own.