Two economic issues and one cultural seem to account for the differences between the UK and US systems.
The cultural first, thrift, especially in Scotland, which affects the economic factors.
Old UK clubs, some on common land, have a relatively low basis. With lower maintenance costs for a variety of reasons, they don't need much relative to most US operations.
Supply and demand. At the high end , there is great demand and limited supply, especially for Classic era "big name" clubs. And Americans seem to be willing and able to spend more on things such as golf, big houses, fancy cars and restaurant meals.