Well... its gonna be difficult to put my thought process into written word, but ima give it a try.
A single break period allows you to perform about... 20 interactions, with change. You can spend them any way you like, but i tend to plan out what i want to do - particularly in the early game. I have a "build order" (if you wanna call it that), and in the first few days of the game, i follow it, more or less, to the letter. Then some jerkwad decides to murder someone, and im interrupted mid-task. I find this horrendously annoying (almost on the same level as some NPC interrupting you having sex for no reason, other than their trait prompting them do to so - "wHaT aRe YoU gUyS dOiNg?!")
Then, as ive mentioned a while ago, theres the matter of me playing for one or two days, and doing something else afterwards. If im forced into another day by a murder - thats not great.
But, i think, the greatest issue i have with skipping days is MM. Its very situational, but it happened on one or two occasions.
So, imagine that you just got into a relationship with a high virtue chick. MM, being unpredictable as it is, suddenly decided to shower both your girl and some schmuck with enough love count to get into a relationship, due to them interacting once or twice when you werent looking or even expecting anything to happen (by that i mean you watched the statue, and only saw "Dont know" as their mutual status, but after one random interaction, it jumped up to "Overflowing love!" without you noticing). They get into a relationship - you think to yourself "easy - i just shoo the guy away; i have 3 days to go about it"... and then due to a random murder the day is skipped. You now have 2 days to shoo the guy away (or rather, 1 day, given how the game counts these days). The next day comes, you have chased the guy off one or two times... and ANOTHER murder happened! Another day skipped - you now have NO time to prevent them from becoming sex friends (NPCs have a unique interaction that cant be interrupted, involving asking the other to have sex - red circle under their feet until its finished). Enjoy.
Time is a resource. Whether its a game, real life, or anything else. And of all the resources we gather and spend during our lifetime, wasted time is the most expensive one.
Its also one of the reasons why i only have two NPCs capable of committing murder in my deck - i dont like interruptions, and the only time i put them in the roster is if i play polygamous and dont care. Ive even removed the killer module off my PC - what it does isnt exactly amazing, since i can just kick the cards that are hopelessly singled out, without skipping days.