And just as a counterpoint to your $10k customer needing to choose between things, there are hundreds and hundreds of customers who lose every penny of their $10k and start over from scratch. (That is what is in the podcast episode, if you have yet to listen.) By imposing the extra process and expense at the beginning, the customer can guarantee some forward progress toward their goal instead of trusting the dev shop to deliver everything by the end in a big bang delivery.
I think if you have a $10K project and you know that you are going to be really, really tight on resources, you don't skimp on the build process. Rather you back up and choose tools that are proven and reliable. If you can't get your 1 click (or equivalent) build process up an running in a day for a $10K project, then you have selected tools that are much too risky. That's my 2 cents, anyway.
Another advantage of a "one click" build process is that it documents, perfectly, the product. What lives where, maps to what and how, how each element is configured, etc. That "one click" is your way into the whole project.