The idea of describing the benefits one gets by singing all the songs could well be the norm in those days. Need not be 'thambattam'. Even the azhwars sung like this. The famed Tiruppaavai by Aandal ends like this "..kothai sonna sangaththamizh maalai muppadum thappaame ingi parisuraippaar... ....selvath thirumaalal engum thriuvaruL petru enburuvarembaavai"
The saatvis always preferred everyone to be happy than themselves so they might have thought by singing benefits like this, it could well be bestowed on the reciter. "Vaakup palitham" may have been a factor. The science of constructing Tamil songs in a particular way (aRam paaduthal) and achieve the desired results could have been an inspiration. Pardon me for any mistakes and please correct if necessary.