Your cycling fallacy is…
“You need special clothes, bags, etc., to be able to cycle.”
In countries with well-developed infrastructure which enables cycling journeys, people travel in normal clothes, without any extra equipment. Racks, panniers and baskets can carry luggage, and chain-guards and coat-guards hide moving parts from loose clothing.
The extra equipment that is often considered essential in countries with low cycling rates is due to the conditions in which people are expected to cycle, rather than something inherent to the mode of transport itself. When cycling is properly designed for, it should be as easy as walking.
Source: As Easy as Riding a Bike (Copyright, used with permission)