Why wooden tees fail on hitting mats.
Mats are a grass-and-rubber sandwich. Wooden tees cannot insert. Here is why.
The layer cake
Every quality hitting mat has at least two layers: synthetic grass fibers on top (5 to 15mm), and dense rubber underlayment beneath (10 to 25mm). Some have additional backing for stability.
Why wooden tees fail
A wooden tee needs soil to grip its shaft. Synthetic grass does not grip. The rubber underlayer is too hard for the wooden point to penetrate. So you have two options: push the tee through the grass until it sits on the rubber (it falls over), or jam it into a pre-cut hole (mat damage).
What golfers do instead
Most mats ship with a rubber tee holder (small flexible cone, glued or socket-mounted). It works at one height, mashes flat after a season, and damages the mat where it sits. The Better Golf Tee solves this by sitting on the surface with no penetration required.