I think all harem stories are inherently nonsensical, but at least this one is a lot more honest than The 100 Girlfriends story's attempt to make them all the MC's soulmates.
Here he's just having sex with all of them, and maybe also learning a bit about each of them in the process. The pacing is really damn fast though, so I don't expect this manga to last as long as The 100 Girlfriends has.
Also, there being 108 fragments, which is the number mentioned in the title, but only 107 girls, is interesting. I know he started off with one of the fragments, but that number difference with the title might imply that he'll stay with one specific girl at the end.