I'm not sure I understand your argument. You can defer maintenance but school, police, firefighter, etc spending is constant. If your infrastructure is in trouble and your budget can't pay for the maintenance, you can limit the costs to 5% or 10% of the budget, but your infrastructure will continue decaying.

Los Angeles has about 7500 miles of roads. At a reasonable cost of $5 million per mile that is 37.5 billion USD. Assuming a lifespan of 35 years, that is basically a billion USD per year spent on servicing road infrastructure costs. If they don't spend that billion every year or put it aside for future repairs, their road infrastructure is going to decay. It might not sound like much in comparison to the full budget, but since the road network is the largest man made structure in the city, it will affect everyone and be the most noticeable failure on part of the government. Lack of police or fire fighting can show up in the form of stochastic damage that doesn't necessarily impact every citizen directly.