Like you say: days passing increase corruption and lewdness, it's the core mechanics of the game.
There are other differences. For example, there's an event, the Festival of Greed, that happens after the first few quests have been done: you actually choose when it happens, based on how long it takes you to do the initial quests (and doing those quests depends how fast you grow strong enough to do them, which itself depends on the difficulty setting you chose, what stats you increased, what skills you pay to learn, etc.). This Festival of Greed is directly followed by a small aftermath, with some NPC's giving you some rewards (money, items, etc.); those rewards will be marginally better if the Festival of Greed happens early enough (before Day 20? can't remember), but the key word here is «marginally».
Similarly, after Day 100, some bosses regain their strength and become more difficult to beat – although if you unleash the full power of Star Knightess, beating them is trivial.
So if you're trying for some absolutely optimal bad-ass play-through, absolutely every day counts. But if you're just playing to have fun, it's OK to lose some time too.
Like the other guy answered to you, those very first «normal» books at the start of the game may have more value if you gift them to your companions, but it's for you to decide: no choice in this game is objectively bad for all players and all play-throughs, every choice has pros and cons