Rav Schachter also Paskens (I think he published this in Ginas Egoz) that you are Over on Bal Tigrah if you wear Lavan without T’cheiles and therefore he says that it’s better to wear no Tzitzis at all than to wear Lavan without T’cheiles.
And the berdichiver would mistama say that is why all the non frum men don’t wear tzitzis. (I’m not sure why he would say the non frum women do wear tzitzis.)