The point of having something -- wood mulch or rubberized surfaces (usually made from recycled tires) -- under playground equipment is to ensure safety. If a child falls from a structure onto dirt, the chances of the child being injured are greater than if the child falls onto a softer surface and yes, that does include wood mulch.
I found this online: "A 2001 playground injury study conducted by the U.S. Consumer Products Safety Commission (CPSC) found that, of the roughly 50,000 injuries annually associated with home playground equipment, 69% of the injuries were a result of falls to a non-protective surface below the equipment."
That's for homes; read this from the National Safety Council about public and school playgrounds:
"Because nearly 79 percent of playground injuries are caused by falls to the ground, improper surfacing is the first thing parents should watch for when they inspect a [public or school] playground. Wood chips, bark mulch, wood fibers, sand, pea gravel, shredded tires and rubber mats cushion falls well. Avoid concrete, grass and dirt, they're too hard. A minimum depth of 12 inches of material surrounding each piece of equipment in a 6-foot fall zone is recommended. And regular maintenance is also crucial; if not daily, then at least monthly."
The wood mulch is there to protect your child. Sorry, dirt lovers who posted, dirt gets packed down as hard as concrete and can hurt almost as much. The solution here is time -- maybe as you son gets older he'll fall on his hands less, or get right down on the ground less, and there will be fewer splinters. And talk to him about why it's important not to play with or throw around the wood mulch. Also if he's got splinters in his socks -- is he taking off his shoes on the mulch?
It's there for his safety and your school system probably requires all schools to have it, or another surface like a rubberized one, under play equipment.