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.
I was honestly really touched when I finally triggered Cass's high approval scene and we were both able to, officially and almost shyly, mutually agree that we were hoping we could call each other friends. Cass is very similar to Cullen in that she's very stoic most of the time (but a sweetie at heart), so it made sense that we wouldn't look super chummy but would have a solid friendship based on trust and respect. It was such an honor to be held in such high regard by Cassandra because I just find her so compelling.
Dorian's presence was really comforting because he's so warm, and I really appreciated that he was able to openly and genuinely declare that we were close as friends. Maybe it's the introvert in me, but though I'm not shy in general I'm actually very shy about displays of affection myself so it was comforting the same way it was comforting that Alistair took the initiative when it came to the relationship. I adore him to bits and I just really want to see him end up happy.
I like to headcanon that Varric was working his way towards a closer friendship with me and that we just hadn't had the chance to hang out outside of Inquisitorialness duties the way Cullen says he's never talked to the Quizzy outside of work related matters. I wouldn't want to ever replace Hawke (and doubt I could) but I imagine we get closer later and him inviting everyone to Wicked Grace was his attempt to get closer to all the people he was working with.
And Cole is just too precious, I want to protect him and feed him nice things and sing "I can show you the world" to him (in a completely platonic way, of course)
I agree about Solas as well - I think Solas is far more comfortable with spirit friends because spirits have a purity of purpose that only others can corrupt. That purity makes them easy to understand and predictable even in the chaos of the fade. I think it's fascinating because there's a reverse parallelism of sorts - in the real world, physical things are very predictable and it is the spirits (minds) of people that are hard to pinpoint, whereas in the Fade, spirits are what are predictable and it is the "physical" aspects of the Fade that fluctuate and are shaped by peoples' dreams. I imagine he doesn't like the idea of humanizing Cole partly because he wants you to accept spirits for who they are, and partly because he finds it alarming that Cole will also become more complex in nature.