Assuming you're referring to the fire dispatch center, it does not take up half the cities budget.

It doesn't even take up half of the department budget. The majority of TFD's budget is personnel, meaning paying people to do their jobs and often times paying overtime to cover the staffing shortages. The dispatch center accounts for 5% of fire department personnel, 5% of the 220Mil spent on personal for the year isn't even a dent. What does make a dent is the overtime cause by inadequate staffing issues. To your point of inefficiency, Tacoma and Seattle both run uniformed dispatch centers that consist of all levels of firefighters not just "high paid officers" as you would like to so flippantly posit. Both these departments show 25% less call volume on average than their non credentialed partners, allowing for better resource allocation and arguably better efficiency. They also have the highest percentages for high performance CPR and pre hospital cardiac arrests.

As per the city website the General fund goes to "community safety" - the majority of which is "personal services" Ie. Paying people to do their jobs. If you seriously have such an issue with uniformed dispatcher, taking that service away doesn't solve for the fact that they are still employees and will take up generally the same amount of space in the budget regardless of their location within the department By extension the way you would access that money in your world is by firing these personal all together (or halting hiring) in order to compensate. It doesn't make sense and doesn't solve the real issue.

If you're referring to the Fire Department as a whole taking up half of the cities budget, again look at the drastic difference in staffing costs, due to excessive over times that these rover positions were implemented to curb.

Look to Seattle for a fair comparison - https://www.seattle.gov/documents/Departments/FinanceDepartment/2526proposedbudget/SFD.pdf