When you are looking at your city budget... you're probably looking at cash-based accounting:
https://www.investopedia.com/terms/c/cashaccounting.asp
This looks at current costs. The school is a cost every year, so every year that cost shows up on the budget. The problem is that road/water/sewer maintenance often doesn't show up on these budgets because these systems are usually built all at once. Because of this they usually also need to be replaced all at once. To see those costs before they happen, you need to use accrual accounting:
https://www.investopedia.com/terms/a/accrualaccounting.asp
The entire message from Strong Towns is exactly that because cities often use cash accounting instead of accrual accounting in their budgetary processes these lingering issues of deferred maintenance don't show up until they do, and when they do, those costs will simply be too large for the city to cover without very politically unpopular interventions.
That’s absolutely untrue. The only reason companies track depreciation as they do is because it allows them to defer taxation. Public works projects are not paid out of current cash.
Strong Towns makes good arguments about certain things and are critical in a reasonable way of how civil engineering organizations rate the need for more civil engineering works. But the budget discussion makes zero sense.
The biggest expenses for county, city, town, village government are: schools, police & fire, Medicaid share in states that do that, and employee retirement and health. A small/midsize city spends 60% of its budget on police.
Capital projects are capitalized with bonds. Governments have the lowest bond expenses due to tax exemptions. Roadwork is not done in a cash basis. It’s bonded for 10-30 years depending on the job.
Capital improvements don't need to be paid all at once; that's what financing is for. And debt service does appear on budgets. In any case, why are we to believe that e.g. $1B in maintenance that's been deferred for decades is "the" problem when the school budget is $500M/year?