Same for me. I felt like Blackwall put me on some weird pedestal, Vivienne was just trying to use me, Sera was just tagging along to figure some crap out for herself, Cass and Leliana too focused on their own stuff. Even Varric, where I felt like Hawke was his real friend, not me. Bull was kinda a friend, gave good advice and all, but nothing like shooting guns of the top of the citadel with Garrus. If not for Cullen, i would have felt very alone in the game.
But perhaps that is what they wanted. Having to become something bigger than we are to make the stuff happen. Kinda feels like the end of the Elizabeth movie, where Kate Blanchette cuts all her hair to become a symbol over a person. Depressing, really...but I guess I get it.
Miss Garrus 
I didn't feel quite like that. My IQ felt really close with Dorian and Cass particularly, and still fairly close to Varric. It's weird, really, I get that Varric clearly considers Hawke to be his best and dearest friend, but when I played DA2 I'd have said Aveline was probably my Hawke's best friend - she knew her longer, and they were like sisters (weirdly, more like sisters than I felt with Hawke and Bethany...Bethany seemed so odd and distant after she went to the Circle. They finally meet again at the end and it's meant to have been what, 2-3 years, in which time their mother actually died, and Bethany was just sort of like 'oh hey, it's you. 'Sup.')
With the others it felt more like colleagues than close friends, or semi-maternal (Cole and Sera, particularly, trying to help them work through some of their feelings and become a bit more mature.) Blackwall I never really warmed to at all, I did very much get that 'put on a pedestal' feeling as you say. Solas I could never get a handle on, weird combination of respect and condescension, but that does make sense for his character, really. I wonder if that's partly why he likes spirits, and Cole, so much; in some ways, mortals, or some of us, are as baffling to him as they are to Cole, whereas spirits I guess are more transparent, for lack of a better word.