I don't think that it's objectifying when you consider that of the likely non-LI men, Blackwall is old and potentially dying, Cole is a revenant, and Varric is taken; all their reasons are external, nothing to do with just not being interested in or being somehow above romance. It also seems to imply that being romanceable is some type of strike against the companion in question, and I don't see that at all.
Not a strike against that companion, no, just the fact that having every single woman who gets close to you open to a romantic/sexual relationship with you, the hero, feels kind of contrived to me. I would say the same thing if every single male were available. I don't know... like I said, it wouldn't bother me overly much, it would just be a bit weird to me. And I rather like the idea of, as Cameron put it, I believe, some of the character having 'no time for your business.' Not that i won't be disappointed if that character is someone I want as an LI, mind you, but when in DA2 Aveline completely ignored my attempts to flirt with her, and Varric told me he wasn't into humans, it made me feel more like I was dealing with real people in my party, instead of characters pandering to whatever fantasy I might project onto them.
Just to be clear, I'm not trying to insult anyone here, I'm just trying to relay my personal feelings, which some other posters I've seen on here seem to share. There's a part of me that would be ecstatic of all the companions could be love interests to all genders, because everyone would get what they want, but it certainly wouldn't feel realistic.