I generally would prefer no more than 4-5 LIs. Anymore than that and I begin to get burned out, even when it's a game I'd like to finish. I encountered this issue with 9 RIP for example, where I was having a lot of fun with the game and eagerly binge playing it, but by the time I reached the last couple of routes I could tell I really needed a break.
I don't mind skipping routes that don't interest me in a game, so too many LIs won't put me off from playing a game, but it does still kinda feel like a shame to not fully finish a game if possible.