I feel like it was inevitable he'd be stuck with her anyways. Just a matter of time before he died, whether it be a few days or a few decades. At least this way he got it over with and can hurry up with adjusting to his new afterlife with her. Sure, she's possessive and clingy, and apparently she considered killing him or at least harming him, but now she can't kill him and they don't need necessities like sleep or shelter so there's no reason for her to ever leave his side. I suppose there's the potential that spirits might be able to harm each other, but it'd be much easier to just accept her. What's the worst that she's gonna do, constantly tell him she loves him and always hold him close? There are far worse fates than that.
Honestly, so long as she wasn't an actual threat to his life it would have been fine to just accept her while they were both still alive. She was so head-over-heals for him that she would have done literally anything for him if he asked so long as it didn't include breaking up or no longer being together in some fashion. She could be the perfect(albeit extremely possessive) wife who would always love him, take care of him, and raise any children they might have without complaint. The only cost would be to never turn his back on her or cheat on her, which if he truly loved her(which seemed to be the case initially) then there would have been no issues whatsoever. With all that said, she clearly was a threat to his life considering she brought a knife with her at some point, so this is all a moot point I suppose.