The game doesn't do well at showing this, but joining the Grey Wardens isn't exactly considered an honour, I doubt especially among nobles.
Dude, what game were you playing? The Grey Wardens are highly regarded in Thedas. Look at Ser Jory, a human knight from Redcliffe who aspires to the glory of the Grey Wardens and actually had to fight in a tournaments and compete with many other potential candidates to get his spot. Look at Alistair's background, which reveals that the Templars put on a tournament to honor the Grey Wardens and hoped the winner would get a spot. (And then felt scandalized when Alistair got the spot despite getting nowhere close to winning.) Look at Orzammar; in both the Dwarf Commoner and Dwarf Noble background, they roll out the red carpet for Duncan and the Grey Wardens. Talk to Wynne about the Grey Wardens and learn of what a symbol of hope, honor, and glory many non-Wardens regard them as.
Heck, walk around Ostagar and most people will show at least a little respect to you for being one of the Grey Wardens. It can be anywhere from common foot soldiers or Ash Warriors paying them respect (even if grudgingly) for being elite fighters, to idiot Jory and Cailan mongering the glory they think they can get for associating with them.
This is especially present if you play an Elf or Mage (even a Dwarf to some extent). The attitude most people have when they first meet you is "Ugh, an elf/mage/dwarf... but you were accepted into the Wardens, so you must be good." Even people who don't like or trust the Wardens admit they don't pick out ninnies.
And, you know, during the Landsmeet the country is steeped in a Blight, and by the end of the Landsmeet the Grey Wardens are going to help save the country from the Blight. Loghain's stance in the Landsmeet is "Ferelden doesn't need the Grey Wardens' help," but you depose Loghain, proving him wrong. And it's clear that by the end of the Trial by Combat (whether or not you won the Landsmeet's initial vote, since people think those who win the trial by combat are "divinely right" since apparently the Maker sided with the one who won in battle) are going to help save the country from the Blight.
Dubious as it is, Loghain getting accepted into the Grey Wardens is still more dignified than getting an ax to the face. Again: going through a potentially fatal Joining ritual still gives him a much better chance of surviving and living to see another day than getting a blade to the throat. Again: the Grey Wardens still have more prestige to join than a blade to the throat. Again: even if the nobles don't necessarily see that much glory or honor in the Wardens (though this depends on individual to individual since the game shows they are largely respected throughout the game), the nobles still acknowledge that the Wardens are needed to help stop the Blight.
Loghain joining the Wardens to help stop the Blight? Gets more brownie points just by virtue of doing that than if he just got an ax to the face.
The way my city elf looked at it, is he can try to redeem himself but he never will. If you have the opportunity to talk to Loghain (after sparing him) he knows he's done wrong and he also knows he'll never be able to make up for it. I'd rather him go through that internal torment than face a quick and easy death. Doesn't matter what the nobles think of it so long as the one responsible undergoes a proper punishment. And Loghain's not the kind of person to like his personal mistakes go. So, to that end, keeping him alive is more satisfying.
Have you actually talked to him as a city elf? Particularly on the slavery issue? He NEVER shows remorse for that. Other crimes? Yeah, wheedle him down enough and he'll show regret and remorse, or at least acknowledge how horrible it is. Selling elves into slavery? Nope, he'll stand by that or insist there's nothing really wrong with it to the bitter end. In fact, he gets mad at you for ruining his slave-trading operation since he lost out on the money it offered. Confront him in the Landsmeet? He makes more bullsh!t excuses and rationalizations to defend it. Confront him after the Landsmeet if you spare him (3:15 - 4:45) ? He becomes dismissive at best, contemptuous at worst.
"Honestly, elf, do you think that among all my crimes that's the one that keeps me up at night? It's a bit egotistical of you, don't you think?" This, coming from the same drama queen who practically froths in rage at the mere mention of Orlais, gets physically angry when recounting what "slavery" he suffered under Orlesians ("How fortunate Maric did not live to see his son ready to hand Ferelden over to those who enslaved us for a century!"), and could potentially throw a screaming b!tch fit at the Landsmeet over the oppression he suffered under the Orlesians. ("Which of you stood against the emperor when his troops flattened your fields and raped your wives?!") But when it happens to other people who are not him or his? It's irrelevant.
What a hypocrite.
Anyway, if you think the nobles' opinions don't matter, I guess you've selectively forgotten that the nobles decide the fate of city elves. Alienages can live well and prosper, squander in poverty and degradation, or die a grizzly death all depending on their human lords' whims. In fact, a lot of crimes and violence against elves happen because those in a position to stop it don't know (as Cailan didn't), don't care, or are the ones actively doing it (Vaughan, Howe, Loghain, etc). A lot of nobles mistreat or neglect the elves because they know they can get away with it. Humans who hurt elves receive little to no legal repercussions while elves who lash out against their oppressors get cracked down on.
So, from where my city elf is standing, letting the latest crime against the alienage fly under the radar (if not mentioned in the Landsmeet) or get brought up just to publically offer the perpetrator a chance at redemption sends a very clear message that it's okay the way they treat the alienage. They can treat the elves however they want, there won't be any serious repercussions for it. At worst, they can have the option to survive and reclaim some lost honor, glory, and redemption by joining the illustrious order.
No thanks.