It is a question of belief. We don’t know the authenticity of our ancestors, who declared that so and so alwar is so and so amsam. When it was declared. Whether it is true or not. We cannot establish it.
But one thing, Mudhal Aazhwaargal, Thirumazhisai Alwar and Nammalwaar did not attach themselves with material life. Kulasekara Alwar was an honest and straightforward Bhakta. Thiruppanalvaar, we don’t have much news about him except that he was always immersed in divine music. So, we can assume that he was also not attached with material desires. The Alwars who were affected by material desires were Thirumangai Alwar, Thondarapadi Alwar and later on were saved by Lord Vishnu. The pasurams of Periyalvar, Aandaal, Madurakavi Alwar (Nambinen madavaraiyum mun ellaam naan), Aandaal involve many bodily desires and explicitly mentions private body parts like Kongai, Algul etc. etc. – these get divine sanctity as these expressions are done towards Lord Krishna.
In my opinion, Naalaayiram Prabhandams are the expressions of personal experiences of various bhaktas. These personal experiences are unique to each person depending on his natural swaroopa. So, they should be studied as Bhakti Literature. Only selected prabhandams, which are of purely spiritualistic nature, should be sung in temples.