1 - False, to your statement of , "It barely takes more effort than checking a box on startup" . . .
That's IF, you find the stamp, during the correct "availability window", ("find her stamp by checking the cabinet with the paint bottles in it in the paint room in a certain time period after she asks for your help"), IF, you miss it, (repeatedly), it gets REALLY annoying & frustrating .
Highland, I really don't want to sound like I'm blowing you off, but the availability window is about three in game days before Himari starts crying every morning about it, and then you have about three days of her crying about it every morning. Grabbing the stamp before it's too late is very easy, even on hard mode, I literally just went to test it myself. I think I can shed some light on this though.
The plot of the game is meant to draw you in to the time loop experience, almost every new player is going to lose to that Himari ending on their first run, because they have no idea where the stamp is, and Erica tricks Himari into thinking you stole it. Some other things to note about these events are that the other girls also give you hints about it's location, and even after Himari first puts you on this bad ending path, it's still possible to escape, if somewhat difficult. Then players either look for it themselves and find it, or look it up online, and find out the spot it's always hiding in every run.
Edit: I forgot, Himari herself actually tells you where it was when this bad end reaches it's end, so anyone that gets it will know.
Now that you know where it is, it's easy to grab as soon as it's first available, yes it's only available when she's painting, but she paints every day at the same time, and you have almost a full week where all you have to do is be in the art room at noon, the only things that can stop you from getting there are random events that incapacitate you, the earliest of which you can probably get are orgasms from the vibrating clit piercing if you "fall" for that little trick. Even then you can just masturbate in the morning and nothing stops you from going to the art room at noon. Plus save states can save you if rng os somehow getting in your way.
A lot of the plot revolves around gathering information during a run to use on the next run. Himari's stamp is the perfect example of time knowledge you can use to your advantage; normally you'd get sucked into the bad ending thanks to Erica, but if you get the stamp, Himari becomes your ally, and you can do it easily every run.
I can absolutely understand being frustrated if you didn't want spoilers and couldn't find it on your own, it's hidden well, but once you know the location, there's really nothing stopping you from getting it the same day Himari loses it. I'm honestly curious if some other aspect of this quest or even the game as a whole is bothering you, because the level of frustration doesn't seem to match the problem.
I guess even I'm annoyed a bit to have to do it every run, but that's the plot, keep advancing on your knowledge of the events to circumvent them and come out on top. Fyi, there's another thing you might want to start doing every run, Katelyn will trap you in a bad end if you don't inject her with DUM+ to stop her, I forget when exactly, but she starts cleaning the house, and gets annoyed at the player enough to bad-end you, but it happens late in the run, so you have tons of time to DUM+ her before that, or befriend her, which I'm actually not sure how to do at all, if it's possible yet.
Edit: Actually I just spotted Katelyn cleaning in like week 2, so that one might start early, but it's still very reasonable to learn her schedule and hit her with DUM+ before it's too late.