For 2020 tax returns, the extension period for NY / NJ and I am sure other states was extended to 01/03/22. Rember that the IRS shut down efiling in early December 2021. For those who pushed it to the end, you could not efile so your only choice was to paper file your returns.
I hope that answers the why paper file question from the perplexed poster and his equally perplexed user group.
