Coming back into this thread after that little joke, the concept presented by the Original Poster makes no sense, at least in my opinion.
If you only want the option for straight/gay/goat/ETC romances that's perfectly fine: you don't have to click on the option that says 'Press X to Dorian' if you are playing a straight character. However, making separate game worlds makes no sense, both from a story standpoint and from a production standpoint.
In regards to the story standpoint, the concept of romance has become a pinnacle trait1 in Bioware games, with characters each with their own likes and dislikes. Removing said likes and dislikes for the purposes of a specific type of 'sexual playthrough' make no sense, as you can simply ignore and not reciprocate those likes and dislikes. To remove those likes and dislikes and allocate them to separate 'worlds' is to remove parts of a character and thus give you an incomplete story. Or worse, you would be changing a characters existence for the purposes of appeasement, making everyone the same just so someone isn't offended. A character should be someone who is concrete; who has their own personality, nature, background, likes, dislikes. No one likes to read about a character who changes their thoughts, feelings, personality, and even history based on the whims of others: That's the work of Mary Sues and bad Fan-Fiction. To make such things fluctuate based on play-through is to reduce the credibility that these characters have and can contribute to the world at large.
To return to my 'Press X to Dorian' joke, and make it more serious: There is a sizable portion of Dorian's character the revolves around his father's disdain for Dorian's refusal to hide who he is behind a set of smoke, mirrors, and a wife. If you had the option of a straight playthrough, what happens to that portion of Dorian's character? Is it just handwaved as never happening, to allow either the player not to be offended, or to allow a female character to romance Dorian? Likewise, are all characters thus changed so that they can be romanced by anyone? Sera suddenly likes men, and Solas will date anyone of any race or gender?
...That's without taking into account the concept of a 'random world' where you could have a Straight Dorian, a gay Cullen, and a Solas who will sleep with anything that's not an elf. All these variables, and all these ruined characters...for what purpose?
From a production standpoint, this means a LOT of extra and unneeded work. Not only would you have to record even more dialogue after ruining the integrity of these characters, but you would then have to have these changes recorded in the Dragon Age Keep under a 'sexuality' tab:
'Did your Inquisitor partake in the Straight only Option, the gay one, or just a completely random one?' How silly does that sound? This whole topic reminds me of a speech made in Metal Gear Solid 2, of which I will let you listen to on your own accord.
I'm too lazy to finish this train of thought.
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1 The writer does not consider this to be a positive thing; hiding a good chunk of some character's development behind a sort of 'romance pay wall'. He thinks there should be a greater focus on friendship and camaraderie than on romance...but that's his opinion, no need to go spreading that about or anything.