Which raises many interesting points. I keep Hawke because Varric likes Hawke and had Stroud come foreword a little sooner, perhaps a lot of this could have been averted.
The problem with Stroud is that the writers didn't gave us reason to make us be more interested in the character, and thus interested in saving him (beyond for seeing what happens if Hawke dies or if you really hate Hawke). People will chose Loghain over Hawke because they care about him, because you have DA:O and some novels to get to know about him. Even if you didn't read the novels, DA:O is enough to know Loghain and care about him. Same with Alistair, and Hawke in DA 2. You sympathize with those characters, and deciding to killing them becomes an interesting choice that will have a impact in your game world.
With Stroud you don't have reasons to like him. Yeah, in DA 2 he could potentially save your sibling, but you don't interact with him enough to like the character. Is just a another NPC. Depend on your choices, he will appear a second time... and again, don't interact with us enough to like him. Heck, he even don't help us in the Qunari invasion, which could make some people dislike the character. And I'm one of those. Yeah, wardens are supposed to be neutral and that garbage, but we know some wardens in Ferelden did help when needed, because was the right thing to do. If you left Alistair in the wardens in DA:O, killed your sibling in the Deep Roads, or didn't take them to that trip in the first place, then Stroud will not even appear that second time and we will have even less reasons to like/dislike the character (we will have more ammunition for the hypocritical Alistair topic, instead).
In DA:I, you get to talk with Stroud in two occasions before the Fade, and his character is as bland and unexplored like in DA 2. You don't get reasons to sympathize with him, and instead reasons to blame him (the wardens involved in the Divine's death). And saving him will have no impact at all for your game world, because none of your characters in DA:I or DA 2 are related to him.
If the writers have given Stroud a better background, I'm sure he will not be the default option for be left in the Fade in game states were there is no DA:O warden ally.