Uh oh...

I don't think I could give you an answer past "No" and stay polite right now. Nothing personal, just too much BSN with too little coffee.
I'll tag in and give it a shot. But only because you are using one of my favorite Ru moments in that gif! (Ru 2016!)
Why wouldn't it work?
Everyone would be happy.
Myself, I would chose straight gameplay and others could chose gay gameplay and others still could chose a mix gamplay.
This wouldn't offend me at all because it would work.
Making almost everyone gay, lesbian and bi sexual isn't realistic.
The developers have already stated that they aren't interested in this option. Characters are developed with a sexuality and they aren't interested in developing characters with 'playersexual' sexuality. Additionally, there are people who find it questionable to have a 'gay toggle' that can be used to eliminate gay content from the game. While that's not the purpose for it from your perspective, there are definitely people out there who would select that just so that they don't have to deal with having 'the gay agenda' 'forced down their throats'. And Bioware isn't interested in pandering to those people.
Also, "almost everyone" isn't gay, lesbian, and bisexual in DA: I. In DA: I, the only LGBT people that we know of for sure are Dorian, Sera, Bull, Josephine, Leliana, Celene, Briala, Harding, and a couple of rando NPCs. That's about 10 characters in a game with, literally, hundreds of characters. If you are referring to just LI's, then it's still only 4 out of 8, which is half (not "almost everyone").