I think it can be a good concept, depending on the extent to which the police force has an extensive budget. Remember, these are folks with massive, massive budgets (budgets that may have exploded over a course of time) that are increasingly militarized and are losing the confidence of the public when it comes to serving their interests. That's how budgets in any public field become ripe for cuts. That's what happens when local citizens become dismayed by actions of the education establishment, that's what happens when a human service sector gets tagged for being internally corrupt with people's money, and there may come a time when technology support services may be targeted because they are taking an increasing percentage of a budget that does not lead directly to services to the citizen but rather becomes a proxy player.
However, it probably will not work as intended. Workers and administrators do not view themselves as unaffected or impartial implements of public policy. They view themselves, rightly or wrongly, as important stakeholders in the procurement and disbursement of public funds. Other local governments who have had to deliver budget cuts may not do so effectively, because those stakeholders in charge of administering policy will try to make the local citizenry feel the pain of the budget cuts--even if the budget cuts would render something unaffected. They then would make sure to tell the complaining citizen "why" a task will be put on the back-burner ("the city commission cut our budgets, so we have to put this on a lower priority"). Whether or not said cuts actually make that task more difficult to complete does not matter. They will try to make it known somehow. And then the pressure will be to restore the agency's budget. And like that, the valve will get turned back on.
I have personally seen a less effective version of this in another governmental sector. The state legislature made a routine habit of making effective (as in not keeping up with inflation) or meaningful cuts (the intentional act of decreasing a budget by a percentage) to the human service agency. In one case, the legislature did not want to "dictate" to agency heads throughout the state government how or where to make the cuts. They just expected a cut of X%. Well, when they gave the discretion to the agency heads, some of the agency heads didn't do an across-the-board cut to programs as was advertised. They made targeted cuts. And they targeted programs that were already bone thin. Or they just outright killed entire programs. Of course, those bone-thin programs could have already landed them in federal court for violating federal law, but I digress. In more private quarters, the agency head said that the reason why they would make these targeted cuts toward already-depleted programs was because they "wanted to send a message to the legislature that you can't keep cutting from these areas and expect us to do all of this work without the resources." Well, that wasn't true when they had more appropriate staffing levels to begin with, but okay, the agency head was telling us they were on our side. Just for the moment though, people who desperately needed services and were to be given services required by federal law were going to go without. So, that wasn't so gracious, as state employees would keep getting a check while people were dying. Anyhow, their strategy ultimately didn't work. The legislature didn't notice, because the people most hurt didn't have the means to complain incessantly to their representatives and even if they did, legislators barely have time to figure out the basics of government programs before voting on them in the legislative session anyhow.
But yeah, your government employees will try to make the public hurt for cuts given to department budgets, even if the cuts are justified or are part of measures instituted to make them more accountable to taxpayers.
It's because of this dynamic that Minneapolis has a number of city commissioners openly flirting with the idea of scrapping the police force and starting over. I don't think that's a good idea in the slightest, but you can see why the frustration is palpable.
