I don't argue, but this unfortunately ties back into the fallout regarding Anders. If they opened back up the idea of companions hitting on the player first, they would probably do it with the gay male characters as well as the female characters. Which I fully support. After all, how would the characters know if you were straight or not? Heck, I agree with you and so does David Gaider for that matter. That was what was going through his mind when he wrote that Anders would hit on the player first. He also thought it was a little silly to keep having the player make the first moves.
While there were folks that were really upset by the rivalry hit (meh,) and those that thought male Hawke came off sounding too much like a jerk (can't argue too much there,) there was sadlyenough protest against the idea of a male character ever hitting on the male PC that Gaider said at the GDC panel in 2013 that he isn't going to have the companion make the first move in the foreseeable future.
As I mentioned earlier, I can't see BioWare doing this again until maybe DA5.
As for your second ideas about the people of Skyhold, that would be a Word Budget killer. The writers only have X amount of words that they can have for the entire story. A small portion of that is dedicated to romances. A lot of this comes down to how much needs to be animated and voiced and then tested. This was the reasons Gaider as well as Patrick Weekes gave for not having a polyamorous relationship among characters. They tried, but it exceeded the word budget and then some.
As to your third, I feel like I've gotten that one already, but YMMV. Could you elaborate further?
I had no problem whatsoever with Anders being flirty, how could he have known? I just wish that there had been an option to let him down more gently. Personally I do not see an issue with gay characters making their interest in me known.
Well, word budget is a good argument but I wonder how that budget would change if they were given more time to finish their games properly. BioWare tried to copy Skyrim, why not copy that part as well? 
Well, despite all that is being said, in the end your companions are still somewhat player-sexual. For example, Cassandra is straight so as long as I am male and win her approval on mostly political subjects, she'll fall in love with me and sleep with me. If it was that easy in RL, then I'd never be single again. 
I would like to have a companion whose "type" I am but who just isn't attracted to me. For example, how about a Dorian who just wants to be friends? Or a Josephine who thinks I'm wonderful but doesn't love me? You know, like how you can be friends with a "sexually compatible" man or woman in RL? Sometimes there just isn't any attraction there. No chemistry.
I am not sure how one could implement this, perhaps a start would be to define your sexuality during character creation?
I think that would give them a bit more depth. I always felt it was a bit weird to be given options. "Do I seduce A or B? C is really cute, too." Meh. I'd prefer if they had lives on their own, without depending on me and my desires. Tali and Garrus hooking up was brilliant, they are a much better match than either one of them and my Shepard. The only flaw there was that the game waited until you made it clear that neither one of them was an option to you any longer.
Imagine them having a drunken one-night stand in ME1 and then listen to their banter during ME2 before they become a loving couple in ME3. Wouldn't that be great? I mean, except for the people who wanted an adorable quarian in their bed. I still have no idea how kissing Garrus would work btw. He doesn't have lips.
Watching and helping Aveline to get her happy end with Donnic was so much fun, I'd like to see stuff like that more often.
You could go even further. Perhaps the person you fell in love with is flirting with someone else. Or is already in a relationship. Now you have the option to try to win them over and possibly upsetting your friends or to wish them happiness and watch over them. Perhaps they do break up later, who knows?
Yes, I am aware that these things are next to impossible to implement. I can still dream though. 