DaasYochid,
This is simply incorrect. Read carefully the teshuva from R’Moshe you cited. The Rambam and the Rif hold that hair is not erva for shma and still hold there is a chiyuv to cover hair.
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The standards for kriyas shma and tefillah are higher than the standards for just walking around or seeing (e.g. one can permissibly view one’s spouse in a state of undress but cannot daven in front of her).
The issur of a married woman not covering her hair at all is separate from dinei erva and is learnt out from a possuk by Sotah. It is d’oraisa. See the Kesubos 72a-b. The rest of what we normally understand as tznius is d’rabbanan.