If memory serves, he asked Carla to kill him if he ever becomes a tyrant (or something similar). It may be just me, but that doesn't seem to mesh well with the whole husband-and-wife relationship.
Yes, I disagree that it would prevent a husband and wife relationship. That position assumes that if a husband or wife suddenly turns evil then their spouse is somehow obligated to not act based on their moral compass and can't stop their significant other from continuing to perform evil acts. Yes, even if it means putting them down. I could make an argument that a husband or wife might do so out of love because they no longer want to see their loved one corrupted by the evil they've embraced, etc.
I'll also add to this that I thought that was a weak thing MC did. Let me explain. Carla would be the least likely to kill him, for whatever reason based on what we'd seen of her character up until that point. MC was basing that on the fact that she quasi-hated him in that moment due to everything going on with the civil war and the rhetoric behind him not being a rightful king, etc. He hadn't factored in that by then she was already starting to soften up to him after seeing his actions, etc. But if memory serves, Carla specifically said to MC's face after he made the long speech about sacrificing himself to Amadonia's (spelling) King that she would do everything in her power to make sure he stays alive for the sake of Liscia.
So, TL; DR version: Carla wouldn't kill MC because of Liscia UNLESS she told her to do so.
There were better options if MC wanted a hidden party to take him out if he went rogue. The Black Advisor/Minister dude who is far more pragmatic, George who MC has operating as the black ops team leader, heck, even based on how she went against her father who she thought had become a bad leader, Roroa would likely go against him faster than the others if MC turns into a bad leader. And I'd even throw in Juna who is a member of or leader of the Navy's special forces marine corps and was acting as a spy before that was revealed to him, etc. etc.
I think MC said that to Carla when he was having an emotional moment and not fully thinking. So, I don't think that should be really used as a roadblock to growing their relationship. But, of course, I'm not the author.
If so, thats incredibly disappointing
Not sure how badly you want to be spoiled about the rest of the story, I'll just say:
Up until he has children with Liscia, Carla is still pretty much just a slave-maid who is a unique servant to MC and Liscia, but mostly Liscia, and acts as the direct caretaker and guard/protector of Liscia's and MC's children. Keep in mind, this is assuming the Manga (and anime) follows anything in the LN or WN.
@SunSerega, I think
@7AlphaOne1 did a far better job answer the issue about the air magic engine than I could.