Warnings are just noise, so there's no point in printing them--they will be ignored (maybe not when there is a singular warning, but if warnings are allowed to accumulate beyond some manageable threshold). If a warning is worth printing, it should be treated as an error, and if you treat it as an error, you now are "strict" by definition.
Any reasonably good C code I ever worked with aimed to be warning free. But yes, if you can also make it an error. The flexibility is important though.