I see what you are trying to say, you want this controversy to bring them closer and end with a legitimate wedding, I will address this in a second.
However, there is a very simple and fundamental flaw in your logic. Karin being the mother cannot possibly be a good thing for Sasuke and Sakura's relationship, simply because it would mean Sasuke was not faithful and committed to Sakura and his gesture in 699 was deceiving. If Sakura is the mother, it would consolidate his commitment to Sakura and his gesture in 699, proving that she is special to him. It is that simple, really 1 + 1 = 2.
Now lets go back to your reasoning, now first of all we have very little information on what exactly happened since Sasuke left the village, we do not know what happened in the past decade and why Sasuke is away, the possibilities are Endles. But let's assume your scenario, which is that Sasuke is not married to Sakura and they are not interacting at all and we need drama to bring them together for a real wedding.
Still, the baby can either be Sakura's or Karin's (both out of wedlock) and we can still end up with that same happy ending, and it being Sakura's is much better. Sasuke coming back, knocking up Sakura, and leaving for 10 years then coming back to start a serious relationship is better than Sasuke coming back with Karin's baby, giving it to Sakura, leaving for 10 years then coming back to start a serious relationship. Because like I said before, it would at least show faith.
I agree that a plot device is a good idea and this is what Kishi is doing, but we can also have one without Karin being the mother as I mentioned in my last point, and it would still not be a wasted chapter. Let me reiterate.
The whole portrait controversy would be a plot device to provide closure to the biological mother "mystery" and make SS more legitimate.
And we have another plot device, it's called Uchiha Sarada. If Sakura is indeed the mother and SS is for real, then it's quite clear that Kishi is using Sarada as a plot-device to deliver our thoughts as readers, since we think SS is "not believable" like you said, Kishi is addressing those issues through Sarada, by having her question her mother's marriage and call out their relationship. By doing that he is pointing out the problem, and giving himself the opportunity to fix it, now that Sarada asked, she will receive answers, and so will we.