Elephant in the Room

Josephine was likely intended as the "conventionally attractive" woman, but it seems people don't like her for... reasons.

There's always one weirdo with an ugly fetish... usually due to lack of self-esteem. (Before this offends someone, it's mostly a sarcastic comment) But there are conventional standards for beauty.  You can't argue with that.  Turn on a TV or watch a movie if you doubt it. 

Actually I can.
This would only be true if ALL movies and tv followed this trait.
Which unless you have seen every movie and tv show made in every country in the world you can not tell me that they are the same.

Beauty as you term it -is a subjective classification system developed to get people to believe along certain criteria -your standard.
A standard you believe that seems to come from Hollywood... I feel sorry for you if you believe such a horrid belief system.
For even in Hollywood this mantra "standard for beauty" does not hold water.
There are movies and even TV where this is not the case.
Especially in other countries where being thin is still considered shameful and being overweight is still considered pleasant.

In short there is no such thing as a "standard of beauty".
For it depends on when, where, who and how you grow up as well as what internally defines true beauty for you personally.
Something obliviously different from where I grew up where appearance was not important at all when compared to intellect and gaining knowledge.

Thing is, I do not remember Bioware ever giving the player the option to romance obese or otherwise universally ugly characters. 

All of this is just a matter of taste, its a non-issue really. 

The day we get LI's that weigh 300 lbs with hook-nosed zit-infested faces is the day I agree with those that say we get universally ugly love interests, which has nothing to do with taste.

Just Sera really.  That's who I'm talking about. The others have been fine. 

EDIT: But some others could have been improved for sure... like giving Vivienne hair, giving Josephine less of a hooked nose, etc.  The men needed work too... the original concept art for Solas was amazing, instead we get a bald alien.  But Cullen, Dorian, Varric and Iron Bull all had the muscled, traditionally attractive looks for men.  Even Blackwall.

The problem here is the ''super model effect''. Have you ever read a womens magazine with lots of top models in it? Then you know the lasting effect those models have on you, which is none - you cannot remember them 15 minutes later or even tell them apart because they all, -while being very beautiful- look completely and utterly forgettable.- Its those tiny quirks and special features that might not be immediately associated with features for the perfect face that makes faces memorable, gives them character and makes them exciting- and ultimately beautiful.

I think that is what Bioware tries to achieve with their characters, with various success. I think, in the case of DA:3, they really hit the nail with Cassandra and Solas. 

Why stop at sounds and personality, the visual effect must not be underestimated, the combination of all those things is important. While I agree with the memorability of the characters you mentioned I have to say that giving them a less generic look would have made them only better. I liked the Characters in origins very much but I have to say I found Liliana and Morrigan, awesome as they may be, visually a little bland. Beautiful for sure, but a little generic - but I think that was because of the limited capabilities of the engine itself. Now that Bioware has better engines they are making more complex and less 'generic' looking characters.

Personally, I am happy with Biowares approach, I like that they are trying not to make every LI look like a Tomb Raider spinoff or like one of those dime a dozen forgettable super models.
And yes, this approach does occasionally produce characters I do not find visually appealing, but at the same time I also get characters that I find very appealing and interesting. I like that they're not playing it safe , for me it totally works.  

CONVENTIONAL BEAUTY! Cause opinions are ever conventional.

Yeah, the games media. My point was that no mainstream game news sites talk about hetero male rage as one of the reasons for all the hate, when clearly it was.

If the rage of males "threatened" by so-called "ugly" women (where "ugly" is construed as anything deviating from supermodel standards) is enough to sink a popular video game franchise, I'm not sure catering to their tantrum is the best solution to the problem. It doesn't work so well with toddlers--yielding too often to such entitled aggression means your kid will be a piece of shit as an adult.
Maybe we should instead just let video games die. Then maybe people will have more time to read some books and get a bit smarter.

Isn't it canon that she does cut her hair herself? I believe there are banters with Dorian on the subject.

It is.