Same here on all accounts, thats where I cut my teeth when I first started playing. With the same stuff being used under the pins you got some real bad skips off that stuff. Thankfully the course is all concrete tees now.
I pulled a hammy on a tee pad in the spring. That sucked.
I have mixed thoughts on the issue.
I slipped on a decent concrete tee pad because my shoes were wet and I didn't dry off the soles or check my traction. Anything grippy enough for that would suck under normal conditions. "Too much traction".
If it's raining, the tee is going to be wet. Unavoidable. Does put the responsibility on the player to compensate.
A groomed concrete surface is about the best compromise I guess.
Natural dirt does okay but rain = mud.
Just about any surface type can become slick if there is water.