You mentioned that Rav Soloveitchik’s wife didn’t cover her hair. RABBAIM said that she had a medical condition which prevented her from doing so. What I do know is that Rav Soloveitchik held that women are obligated to cover their hair.
The Rav Thinking Aloud, page 113:
DH: What is the heter for a married woman in her house not to cover her hair when there are outsiders present?
RYBS: She has to cover her hair.
DH: Someone was asking about a woman wearing a kisui rosh in the house.
RYBS: We pasken you should.
DH: Someone showed me a gemara in Kesubos that b’toch chatzeira it should be mutar, since otherwise there is no way any woman could remain tachas ba’alah (72b). Offhand it occurred to me that if it was lo shechichei inshei – just for going around the house when no one’s around, and someone just may drop in – then it would be mutar. But if you have people coming over b’kevius, then why would it be any different than going aroung in the street? Is there a special din in the bayis that there’s no din of covering your head anymore?
DH: Is this kisui ervah like most kisui ervah?
RYBS: Of course.
DH: What should I do for myself, for my wife?
RYBS: You will find out.