The decision to do the DR in order to save your Warden's life is a rational but selfish one. Not only is Morrigan not a "people person," she seems to be very much an "anti-people person." Think of all the decisions you make during the game for which Morrigan weighs in. In order to get a 100% from Morrigan, you have to not help everybody you run into, you have to desecrate the Sacred Ashes (betraying the trust of the Guardian and all to win the favor of a nutty cult), sacrifice the lives of imprisoned city elves in order to get some magical bauble that the Tevinter slaver would make for you, etc. This is the person you are going to trust with a child with the soul of an Old God? She doesn't even seem to care whether the Blight is stopped at all. If you opt to do the US, she abandons you and the rest of the team. Not a person to be trusted...
There are a finite number of Old Gods and thus a finite number of future Blights. By doing the US, you guarantee that there is one less Old God/AD. By doing the DR, you create the possibility that one of these Old Gods/AD will make a repeat performance in the future, thus negating the sacrifices of all those who fought to kill it the first time around.
As to Morrigan being your warden's LI, people frequently make bad decisions when they fall for someone of questionable character. Such mistakes are understandable but still mistakes all the same.
Just want to correct your position about Morrigan, haven't read how others might've answered. Morrigan isn't really 'of questionable character' so much as she was just brainwashed by her upbringing (which really was a harsh way of pushing pragmatism, isolation, and power for Flemyth's sake, not Morrigan's). Those are Flemyth's rules, not Morrigan's character. You can break that down over the course of the game as either a lover or bestie. Morrigan's actual character is reasonable, socially reserved, inquisitive and fanciful, which is why she resents her upbringing so much. You can easily get 100% with her while helping everyone you meet, doing none of those negative things you mention. She's got the best potential arc in the series. Yes she'll react negatively, but typically to the tune of 1-3 points when you explain your position. Cracking her shell and overcoming Flemyth's influence is the great draw in her story. Love breaking down those walls. Morrigan appreciates a positive relationship with the Warden more than any other character, I think, and she's bluntly, almost compulsively honest throughout. Morrigan never gives you a reason to distrust her. It's true you can sleep with her early, and she has ulterior motives at that point, but it also weighs on her, which is why she'll cut a love path Warden off at a certain point, and why she approaches you honestly at the DR junction. She doesn't have to. She's not disloyal by nature, even though she is distrustful. She is impulsive, evidenced by her theft of the forbidden vanity mirror as a child, which also manifests in how she pursues the well of sorrows so strongly without really knowing what it is, among other things. But she's not really ultimately selfish. She will self sacrifice for her loved ones and the potential greater good. She just has a little more knowledge than most, and as the saying goes, a little knowledge can be a dangerous thing.
Edit: I think this all applies to Morrigan's reasons for going through with the DR herself as well. I mean, she pretty well spells it out for her part. She knew something was coming, she didn't fully understand what. She spent half the game trying to decipher her mother's grimoire, after all. She makes it clear this is part of what she's been working at understanding. She knows Flemyth doesn't die so reliably, she's some kind of ancient terror (from her perspective), and she would likely show up again when least expected. And in the final calculous, she wants to save her friend/lover's life when it comes down to it. So she very clearly lays out the why from her perspective. It's just a question of whether you trust her or not, and whether you care about what happens to her later or not. She even tells you exactly what she plans to do with the child: raise it for her own. Prepare them to defend themselves. Not risk losing them all against the AD. If you refuse the DR from Morrigan's perspective, you're betraying her trust and friendship, which is why she'll leave and look out for herself. Then Witch Hunt rolls around, and she'll flat out take you with her if you choose. Again, it's a rorschach test. Do you trust Morrigan or not? How much does your Warden care about her and the baby? Enough to leave behind whatever they've achieved since Denerim? She's not actually keeping any secrets from the Warden.