The jail then needs staff. It needs maintenance. It needs utilities. The monetary needs just shift from construction to operation.
It probably didn’t pay for a jail: it paid a loan for the jail, and it will take many decades to pay off
In addition to staffing that other people mentioned, your town isn’t paying for the jail up front. They are issue a decades-long bond and paying off construction over 30+ years.
Edit: then after the bond is paid off, they sneakily move the tax to a general fund for other services
Simply put because they want more money. Even though the jail is paid for at some point. They’ll just keep the tax and keep collecting and then spend it on something else.
Want to hear something that’ll really piss you off? Every year or a couple years and they’ll replace furniture and computers in city offices that don’t need to be replaced. It’s totally in workable condition but they’ll spend the money anyways. Their argument is well if they don’t spend the money then they won’t get the same budget next year so they have to spend it now and yet the reality is they don’t need the equipment.
Then the city turns around, spends even more money on other crap they don’t need and then raise your taxes. Claiming They need more money.
edit: i’m getting down voted because I had a few typos that made it sound like they were spending money on things they DO need. My bad. screwed up typing is now fixed.
People are giving answers to your specific hypothetical, but on a higher level, the answer is simple. The government likes having more money. Once a tax is in place, it becomes the new normal. It can be like pulling teeth to make a government roll back a tax. Groups in my local area have tried numerous times to roll back a specific tax where a government spokesperson has even said the tax is no longer fulfilling the original purpose, but removing the tax would now affect the overall budget. That has become the reason they refuse to remove it, and because neither party cares much about removing it, there’s no political leverage by the voters who care about it.