The "shiny side down" scenario is why you have the insurance. There's no other reason, really.
We used to rent a lot at a ski resort for $250. Fair chunk of change to use a disused parking lot, really, but consider that for just over $500 we could run an event. Split that $500 over a couple of dozen drivers and you're looking at $20/head. There's a local high school that will let you use their lot for free, which obviously changes the budget quite a bit. It's in high demand as you might expect, but get in line at the beginning of the season and you can use it for a few events. It's what the local Corvette club does.
Fear of pavement damage is the usual excuse for why venues will turn us down. Then I have the venue talk to my wife, who's the head estimator at the biggest paving company in town and actually was in charge of paving most of the venues we approach. That usually shuts them up. The local fairground does more damage to their lot by having loaded pickup trucks parked on the lot in the August heat than we do by running little sports cars over it.
We don't use axware. Our timing system actually can interface with a laptop and export results in a spreadsheet - but it was a hassle to set up, required specialized knowledge to operate, could only be viewed by one or two people and was a bit cantankerous. Now, we just have the stopwatch taped to the side of the starter's truck. When the time comes in, you write it down on an address label and stick it to the big sheet of paper with all the times on it. Everyone can walk up and see all the times for every car, anyone can play the role of starter. Works a treat.
You can make this sort of event as complex or as simple as you like. I prefer to go for the latter. People still have a lot of fun and it's easier on everybody. I don't consider it expensive or difficult to put on an event really. But that's because I've actually done it. It might look daunting from the outside if you're looking for reasons as to why it's hard, but it's really not tough. The hardest part is probably obtaining the cones - I got lucky there.

