Bikes definitely have a place in emergency preparedness, but they are most effective if they are of reasonable quality, and are powered by a well tuned, practiced cyclist.

I have commuted primarily by bike since 1970, at distances ranging from 22 miles to ten miles round trip, and lately I have done several solo self supported tours, the longest of which was 450 miles.

I wouldn't try to carry too much on the bike in an emergency situation. Excess weight and baggage negates one of the bike's principal advantages - its ability to be carried over non automotive patches and to worm through slender spots.
You can carry a bit more on the bike, using panniers and bags, than you can comfortably backpack. About forty pounds will travel easily and should enable self sufficiency. The more you use your bike before an emergency, the more useful it will when it hits the fan. Seventy miles a day should be easy for a cyclist in decent shape.

When the Big One arrives in my locality, I would much rather try to get home by bike than by car, as I anticipate that the streets will be damaged or jammed with automobile traffic. I prefer wide (37mm) tires for stability, comfort, and relative freedom from flats, but I always carry spare tubes, a patch kit, pump,and basic maintenance tools.

Oh yes - I wouldn't ride my bike five feet without a helmet, gloves, and a rear mirror.