...Now I'm thinking I will make flaps to cover the pockets - didn't even think about all the **** that will makes its way in there...
Ha! What have I started?
There are a number of woodworking tasks where my apron pockets get stuffed with chips and dust. I can't say I've considered modifying my apron. I'll just flip it and shake it every few years; when the pencils don't fit any more (basically, after every project where I use the router).

I use apron pockets for pencils/markers, and maybe stuff a short ruler or square in there, but they're not conducive to storing small parts, so the sawdust in them doesn't bother me. Especially when my pants pockets are still accessible.
I think that flaps on a pencil pocket will get annoying real fast.
With the lab coat, I have limited access to my pants pockets, so I'll put small parts in the hand pockets, and there, I don't want something like a grub screw or single ball bearing lost in sawdust. Plus, since I weld with it, I don't want tinder in my pockets. I don't use my apron for welding or grinding, since it lacks the arm coverage I would want, if I'm looking for PPE.
Funny thing is, now that I'm thinking about it, my lab coats don't have the traditional chest patch pocket for pencils (probably because of the chemical splash rating). They're this pattern:
Now you've got me thinking about sewing on a strip of elastic to the arm to hold pencils.
That's pretty good, one thing I can't do is sew, do want to learn.
Well, there's no time like the present!