Hmm. I dunno, when I think about it, I don't really see it that way entirely. Mostly they seem like two people already very familiar with each other and it's pretty chill.
Like, she has a key to his house, but knocks most of the time, and is not even over all the time. Hell, for how Shirou focused she is, Ayako is the one who bugs him more to rejoin the archery club, while she just goes there like normal. One of the things I liked about her is that the things she liked that Shirou influenced she indulged in, with or without him. So it males the times the kitchen duo get together that much sweeter, because it's honestly something they both enjoy, not something she does just to please him.
People meme the line up, but Shirou going "oh, Sakura is in the kitchen" is pretty indicative of their familiarity. The kitchen and the shed is almost equivalent to his mancave, and he is perfectly comfortable with her there. It's those rather subtle things that does it for me.
I remember the first time I played the Fate route, and Shirou said that his home belonged to Sakura as well, that was the start of when I really started shipping them.