Our safety codes (and NFPA Codes) require clearance of flammable materials for a significant distance from the launch pad. That definitely includes dead weeds, grass, cow manure, etc. It’s the least enjoyable job of range preparations, but it’s possibly the most important.They most definitely can start a fire at launch and I was personally responsible for one around February 1981 in Orlando unfortunately. We held a contest and I was flying a glider I believe. The large field had tall grass/weeds and they were very dry because it was winter with no rain in a while. We didn't pay attention at launch because we were watching the flight and when someone turned around we saw a rather significant fire had started in the dead weeds and was rapidly spreading. All of use tried to stop it to no avail and I remember after the heat had very slightly blistered my forehead. The local fire department came out and put it out after it had gotten very large. I know of two other instances of large brush fires starting down here that needed the fire department to put out. Be very careful and always keep an eye on the ground after a launch to stop it immediately before it spreads and cannot be stopped. Here's a picture of the Orlando 1981 fire after it was put out, very bad.
If that simple, but labor intensive task is done, there is much less risk of launch pad fires, but as you say, they certainly can happen.