As far as outsiders are concerned, shrI-vaiShNavism stands entirely on the basis of veda alone, even where establishing viShNu-pAramya is concerned (since they don’t care for other pramANa-s which could be presented, like pAncharAtra or the tamiL prabandhas).
They cite nArAyaNopaniShat (and such parts of veda), argue why nArAyaNa is visheShya; why similar logic won’t apply to shiva etc.. You wont find a single appeal to pAncharAtra or prabandhas in bhAShyas, vedArthasangraha (hindi translation here) etc.
As far as the main points are concerned, if one mistakenly thinks that SV-s heavily rely on sectarian texts for their convincing power, one would ask -
If you find nArAyaNAnuvAka unconvincing, why would you find sAttvata-saMhitA convincing?
Whether or not some particular person finds it convincing, it is evident that shrIvaiShNava-s themselves felt veda-only reasons more than sufficient to convince impartial readers.
Anyway, success of SV-s among south Indian v1-s is mainly because of their ability to establish their doctrine on the basis of vedas alone. (which would be unquestionably accepted). Their main rival, the mAyAvAdins, relied almost entirely on veda-s only. You need to use pramANa-s which your rival accepts for a fruitful debate.
The later failure of shaiva-siddhAntins in south India among v1-s is also same - non-reliance on all-accepted veda-s (eg. no brahma-sUtra commentary). This is natural too - their elaborate speculations (36 tattva-s, hierarchy of bhuvanas etc. etc.) can’t as easily be based on just the vedas.