As other have said, its not so much the "storage" of propane, but the "leakage" of propane that causes the problems.

The storage tanks have been around a long time and are well thought-out. Even the house distribution systems are well thought-out - in general. Most propane (and gas) appliances have safety devices that "should" auto-ignite the gas OR that shut off the fuel if a pilot goes out. Note the "should".

Routine appliance inspection & cleaning is a good thing.

Still, with my house running on propane, that does make me think about getting an LP gas detector or two.

BTW, I recall them shooting bullets into propane tanks without real incident on Mythbusters.