We do alternate nostril breathing interspersed with increasing retentions to allow for expanison and greater flow of prana to be accomodated.
The reason that Swami Vishnu allowed pranayam first was because he found westerners will walk out of class if it was rightfully placed at the end. It is experientially more beneficial at the end. A senior disciple of Swami Vishnu told me this recently and it is noticeably beneficial for the serious to practice this way..
The pranayam is heating for most especially with kapal Bhati and warms one up at the beginning we do this and then shavausan to cool down.
Swami Sivananda and Swami Vishnu definitely proposed pranayam after asana but Swami Vishnu had to modify for aforementioned reasons..