I've read books written in a non-continuous style and, while it sometimes took me a while to catch on, I ended up enjoying them.
The first book I think of reading which was 'different' is Sorcery & Cecelia: or The Enchanted Chocolate Pot by Patricia C. Wrede and Caroline Stevermer. This was written, quite literally, as a series of letters back and forth between the authors.
I've since read others which are more like what you mention and, once I got used to them, they're great. (Well, they're great if the story is great. The method of telling the story wasn't a reason for me liking or not liking them!)
I think that, a lot of the time, using an alternative method of writing style introduced elements to the story which otherwise might have been difficult to get into it. Michael Creighton would often put in 'scientific documentation' which, at first, I look at and boggle, and then find out ... oh wasn't that clever!
A very great story told is that of Dream, in the Sandman books by Neil Gaiman. This is all 'comic books', and yet, the very structure of the art, the lettering, the placement of the panels -- the whole thing -- all of that adds to the richness of the story he told (story cycle).
"You have the inborn natural right to remain silent. Don't think about it, don't talk about it, shuush ....... STILL." ~ Xaris