Yeah, it's more of a "highest bidder mentality". That they don't have any experience with hourly billing should have been a massive red flag as that means they need to be very conscious in how they approach the project. That they used this simply as an excuse to deprioritize the project is what caused the problems.
The agency I worked for used to offer a "special" for a brochure site. Basically it was a "website-in-a-day" deal. Customer comes to the agency in the morning, meets with designer and manager, and they agree a design (preliminary work has already been done on a logo). Customer goes for lunch, and the design is handed to two devs. Around 4PM the customer gets sight of what the devs have done, and goes home. The devs work on until say 8PM, and probably put in a couple of hours the next day.
Of course, there was then snagging; it wasn't really a one-day job. The whole deal was pretty inexpensive. We used Drupal with a custom theme.
I don't know whether we made money on these projects, but we did end up with a string of long-term customers.
You can't really imagine anything being completed and deployed in that time.
It was a death trap to begin with. They're experience should have flagged this.
But both are equally at fault. This is what happens when clients have the lowest bidder mentality.
"the cheapest price is always the best option because it's the cheapest."