Yo, it's not like it's impossible. The Binding of Issac told an extremely thought out and detailed story. I'd say the rogue-like nature of the game, slowly discovering new bits of the story over time, made the plot much more compelling. It's definitely not everyone's idea of plot though, so it might not be the kind of thing you are looking for. Other than that I can't think of any other rogue-likes I've played that had a very good story off the top of my head, so it's definitely not a common practice. At least not yet. Plot definitely helps/would help those not familiar and in love with the genre to get through the beginning (seeming) monotony and repetition that by nature rogue-likes have, so in my opinion it seems like a really good idea overall. However, if the game is focused solely on the plot then it might lack replayablility. Just a thought.
I was thinking about the Binding of Issac while I was brainstorming, but I think I would try to have a larger, more engaging plot. You do make a point though, if there is too much focus on the plot and it slows down the game play replayablility goes out the window.
For sure. As someone who isn't overly creative when it comes to plot, I'm not sure I can really help you with that, but if you have questions about gameplay and stuff, I might be able to help. It seems like (from what you've said) that you are looking for a faster pace game. Are you thinking like a bullet hellish kind of thing? More puzzle based? More strategic gameplay? Or a mixture of all of them? You have a metric fuckton of options with this, and with rogue-likes booming like they are, you have a good chance of doing well for yourself if you can make at least a decent foundation for a game. If things go well and at any point you feel it's polished enough to be put out into the indie community, send it to a youtuber named Rockleesmile. He does reviews of indie games and has a good deal of experience with rogue-likes. Hope this helps :D