Was Ancient China so lawless and unruly that you needed to shield yourself, even when just sauntering?
Did Ancient China rain as China does now, so that you always needed a parasol? In Cantonese, 遮 means parasol. As of today, Three Gorges Dam purportedly is overflowing.
One of the meanings of 遮 is "obstructing" - getting in the way of somebody else, thus preventing them from walking. That might be the reason why 辶 (walking) was chosen as the semantic component.
As for the usage of 遮 in Cantonese: It is easy to make a connection between "cover, shield" and "umbrella, parasol" because umbrellas/parasols are used too shield oneself from the rain or sun. In fact, "para" in "parasol" or "parapluie" (French for umbrella) means "protecting against".