I don't know so much about this one. I agree that it can break the thing...
See, the thing is I have only used Inspiration once in the game, to persuade someone to not kill me. I'd made the success after the Inspiration, only to fail on another Persuasion right after that. This felt horrible.
However, I feel like the effort is to make the conversations more 3-dimensional. Conversationally speaking it makes sense not to convince someone in one go. Hence why the low-DC all around, so that the stats you mentioned are respected. In your case, convincing the guy had a total DC of 17, turned into 3 rolls of 7. It can work, specially if failing one of the 3 doesn't prevent you from total success (I'm not sure on that) and if you are somehow prevented from wasting Inspiration on non-determining rolls.