It it bowing at the altar of Mammon to have a career? (An honest question, as I'm not sure what your or Tim's take on that is.) I believe that there's room for being able to make a comfortable income out of something like this, without making the money the priority.
Tim could choose look at it not as "I'm getting rich!", and instead as "This is a way for me to sustainably build something I love and ensure that my users can get reliable updates, because I can do this for my career instead of working at {CompanyX}."
One could likely even charter it as a business where outside a regular salary, the remainder of any profits get donated back (or costs reduced).
It's __certainly__ more trouble than giving it away for free, as you'd need an accountant and worry about taxes. On the other hand, if this is a service that you feel every church deserves good access to if they want it, being able to work full-time on it might make it happen more easily.
As for the churches, I'm sure that many of them pay for services that they feel are worth it. Landscaping, maintenance, etc, are not always something that every church can do in-house, and this service sounds like it falls into the bin of "things people would pay for".