Since a lot of comments I see on here are from the earlier chapters, I just wanna say at the beginning the main character does seems a bit annoying and stupid but stick with it, she doesn't stay that way. She's a bit gullible (to an extent) but that's cause she has low self-esteem. I was a bit worried going into it since I read all the comments but I actually think it's super cute and honestly I can relate to some of the troubles the FL has.
Okay but integrating doesn't work that way? They don't just disappear. Integrating means they fuse. Usually it's on alter fusing with another so the memories of the two alters come together. It's like putting together two pieces of a puzzle. So yes they do change but there are still the memories of both alters and certain attributes can stick around. So it's not like they die, they just change. So saying if it'll be kazuma or rei left honestly if his who system integrated into one, neither kazuma or rei will be there.