I think it's also not just about the emotions of firing someone. It's really hard to manage a downward trend - and not from a touchy-feely standpoint. If you're an uncaring machine and people leave, you fire a proportional number of government employees. But that doesn't solve the situation. Every business in the area now has fewer customers. At some point, those businesses close reducing tax revenue further and increasing unemployment more. It's not just the city that feels the pinch of a dwindling tax base - that dwindling tax base means there's also a dwindling consumer base.
An important thing to remember is that cities/towns/counties often take out debt for spending that will pay off over time. For example, you want to build a school so you borrow $X and you'll pay it back over the next 30 years. You need to rebuild some roads so you borrow and pay it back over the next 30 years. However, if your population is dwindling, that can leave the town holding debt it can't really pay anymore. If you built a school for 1,000 students and then the population dwindles by 30% over the next 20 years, you're stuck paying for way more school than you need with fewer people paying for it. Ok, layoff some teachers - but you have to lay off more then 30% of the teachers because you're paying for 100% of the school debt and maintenance costs. So you fire 40-50% of the teachers, class sizes go up, the people with the best options (the most educated with the best job opportunities and most money) leave your town eroding the richest part of your tax base and leaving lower income people on the hook for that debt while they escape it...which causes you to fire more teachers which causes more people to leave...
I think it's not just that there's a messy human side to it, but that it's hard to manage decline. Ok, you wind down a department. What about the building? Maybe you can sell it, but probably at a loss since you have a declining purchasing base. As you wind down a parks department or library, the richest people are likely to leave. Now your algorithm requires more cuts.
And the sad state of it is that it's often not a parks department. It can be things like roads or safe drinking water.
There is also a messy human side of it as well, for sure, but it's just hard to manage decline. I can totally see the game: you cut the parks department and the rich people complain, sell their house for 15% below previous market value and leave, and your tax base dwindles more. You cut after-school programs and more rich people complain about the town and schools and leave - and your tax base dwindles more. You try to attract new residents to YouVille and cartoon characters say, "I want a town that invests in its schools," and "everyone I know is talking about leaving YouVille."
