How long is "long before the tornadoes dropped from the sky" ? The National weather service has gotten much better at warnings but some times the warning time is as little as 5 minutes (or less). Even with 20 minutes of warning getting people to go to a community shelter would be difficult.
Tornadoes are often found in severe thunderstorms (Hail, lightning, and high winds). Going any significant distance outdoors in these conditions can be very hazardous. Also the inconvenience factor (loss of time, number of "false alarms, not wanting to show up in your bathrobe) would limit how effective a community shelter would be.
Improved building codes would help a lot with smaller tornadoes. Basements and "storm cellers" are traditional in parts of the midwest. Personally I wouldn't own a house in a tornado prone area that did not have a basement. It isn't a guarantee (there are few in life) but it improves your odds tremendously.
Like much else in life - you make your choices and accept the consequences. Choose to live in a flood plain, expect floods. Choose to live near a fault line, expect earth quakes. Choose to live in a house without a basement or storm celler in tornado alley, expect the worst.
-Eric
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You are never beaten until you admit it. - - General George S. Patton