The point is more that by saving those 15 minutes, it's a cumulative saving for all future use cases. Though, I don't think I fully agree with this in all cases. It can be hard to predict when something really is going to be used often enough that this is important.
IMO you build the minimal thing that does the job, then after understanding the use case go back and refactor to deal with the accumulation of 15 minute pain. Doing it right at the beginning is the definition of premature optimization.
And on the topic of building new, this is a mistake many developers make: that it's easier to build new, then to refactor existing. What they fail to realize is that the old code they think is too difficult to maintain is battle tested, in production, has operational understanding associated with it. All software goes through this cycle, and so while it's fun to build something new, you are inviting debt while doing so b/c of the unknown production issues and edge cases that need to be figure out after it goes live. It's not always wrong to rewrite, but IMO, it's a last resort. BTW, this is why SOA is important: strong defined contracts/APIs between services allow for components to be replaced with a higher degree of confidence.