We have solar panels and a mostly electric home, so I also seriously considered shutting off my natural gas service (and I actually prefer cooking on an electric stovetop.) We also pay a stupid monthly "connection fee" to use almost no gas.
The reason we didn't is our water heater. Unless you're on natural gas heating, your water heater uses far and away more gas than anything else in your house. Shortening your daily shower by 5 minutes saves more energy than converting all of your lightbulbs to LEDs. Natural gas is just super-duper energy dense, and it takes a ton of energy to heat up water.
And electric water heaters are pretty dumb. You can get around the inherent inefficiency if you buy a heat exchanger model, or one where the water heater is tied to the home furnace (more popular in Japan), but a standard electric water heater is a power hog. Like > $500/year in electricity all by itself.
So in our case, we decided to keep the gas connection for the purpose of our water heater, and having natural gas back-up to our heat pump.
As a separate discussion, people I know who live on propane all hate it. You have to deal with maintaining the storage tanks and valves, you have to have it delivered regularly, and it's more expensive than natural gas on a per-BTU basis. I think it's really on a viable option for remote cabins and such, where you don't have access to the power or gas grids.