At the local level, budgets matter. Even if you're going to spend your entire budget, spending less on tools frees up more budget to spend on other things. Things like community events, more staff, creating programs to engage or serve under-represented groups, commissioning cross-departmental studies.
Saving time absolutely matters. The common belief is that local government employees are lazy or incompetent. Again, we've never found that to be true. Many of them came into public service to serve their communities — no one gets into local government for fame or fortune — but were beaten down by the bureaucracy.
They are motivated to do good and better back office tools help them achieve their goals.
Maybe its true that saving money isn't a priority, but spending money on things that have the most impact, or that get the most value is a priority.
I work for OpenGov, so I hear this from our customers (who work in government) all the time.
We haven't done any work yet at the state or federal levels, so maybe we'll encounter this attitude there.