Is the Izar (waist-wrapper) obligatory, and if so, why do most people of knowledge not adhere to it?

There is no statement from the people of knowledge (scholars) that wearing the izar (loincloth) is obligatory. What is obligatory is to cover the awrah (private parts) with any covering. The best of these coverings is the qamis (tunic/long shirt) because it is more effective in covering than the rida (upper garment) and the izar.