The question is over a pivot from "I'm going to provide product/service X at a profit due to my tool T" to "Well, I couldn't sell X so I'll sell T to other people who want X". If you couldn't make a go of it, is it really likely others will, or if they can that they will want your tool T to do so?

This is different from either providing a service and successfuly using your own software to do so or providing a service and developing as well tools specifically for your customers.

Slack was suggested by another poster as a company that pulled this off, though I'm not sure the communication tool was considered crucial to the game business.

Fair. I guess it depends on what you determine as a success. 37signals was probably somewhat successful as a dev shop, but obviously not nearly as successful as a project management software one.