Days out.
There's a couple of others who've brought this up before... but it's a bit of a strange critique to me (and seems a bit nitpicky to someone like me, who plays these games habitually: no offense!)
The button you see on the screen, when presented alone, is obviously not presented as a "choice," otherwise there'd be some sort of decision involved. Rather, the button is merely a transitional technique that is actually coded in to
help the flow of the game, not hurt it.
The things I use this for include, but are not limited to:
1) More emphatic transitions, such as going into a new place for the first time, or opening a door to discover something earth shattering... like three new tenants.
2) Letting players know they're about to start some sort of major sequence, such as a sex animation.
3) Giving players a little bit more control when screwing a girl for the first time (i.e., the option to PUT IT IN!!!).
4) Letting players know they're about to start the next sequence in a multi-part sex animation... etc.
While I'm aware that this might be a little annoying while playing with one hand
I think the majority of players actually like this. In fact, it was designed to accomplish the opposite of what you said: more immersion.
Oh, and as for the bug, that might have more to do with your system, as even Ren'Py games can get a little draining on your memory and it sounds like you're experiencing a brief lag.
Anyway... I'll start a poll over on Patreon to see how players feel about using a "Click This" type button/selection as a more dramatic transition. If the majority of players vote against this, I will remove it... though I think there's a walkthrough mod that gives players this option already. I might also just add in the option for players to turn this off at the start of the game if enough of them vote they dislike it.