The sleep buffs start at wakeup (0800ish) and go for 12 hours (until 2000, a few hours after most shopkeeps are closed). They basically extend for the full length of an actual working day, and then some. You can find more than one or two encounters in that time. You can find a lot of encounters in that time. The length of the sleep buffs isn't the problem here.
A perfectly normal CoC2 day for the Champion can start with waking up, then a dozen hours of Normal Adventurer Stuff, whatever that is to you: selling off inventory, buying other inventory, beating up mooks, sexing mooks, doing quests, etc. Then, in the evening, after the sleep buffs wear off, you have some time to do any companion sex scenes you want, if any, before going to bed and waking up again, bright-eyed and bushy-tailed, for more of the same. That...feels like a fairly reasonable use of a day to me. It's not mandatory, but nothing in there sounds like a waste of time or a poorly placed event.
You're not "expected" to do anything. The sleep buffs are an entirely optional part of the experience. So are sleep-withs, dreams, Kiyoko, and so on. If you want to go around adventuring and never sleep save when you level up, that is perfectly fine. If you prefer having the RP, the sleep-with scenes, the buffs, or any other aspect of the sleep-related content, then that is also perfectly fine. And if you want to wait until five in the morning to go to sleep rather than doing it at nine at night, that's also fine.
The current sleep system is an attempt to combine a certain amount of verisimilitude (meaningful difference between night and day, characters outside the Champion's party seem to have their own lives and schedules independent of the Champion, sleeping is actually good for you, sleeping around the normal times is good for you) with concessions to a certain level of player convenience (the player is not forced to go to sleep save to level up, the player can stay up late before going to bed) and writing (sleeping results in a consistent wakeup time).
Why does time spent per day have any meaning to you? The day counter doesn't matter in-game except as a way for the player to tell how much time has elapsed between events (e.g. between conception and birth). You're not racing the clock. If you spend the canonical two or three months on a single save, that's fine. If you spend four hundred years in-game, that's also fine. This feels like a you problem, not a gameplay problem.