All the videos I see of nitro trucks running are always on dirt. Is there any technical reason for not running on well mown, like a park, grass? Not counting the potential noise problem for being in a park but the actual running on a grass surface?

No issues running on grass at all. I do it all the time. The load on the motor/engine is higher so one needs to be careful not to overheat the engine/electronics/motor, but otherwise there's no reason not to run on grass.

I like to run on dirt for the power sliding, which is probably why a lot of videos show that. Also dirt surfaces are usually more bumpy so you can watch the suspension work. I also run on grass well mowed and super tall alike, but it is less fun overall. As long as you're tuned right you have nothing to worry about.