When the Founders were around, government was simple. You made sure everyone didn't revolt, scalped the day's enemies, and drank like every week was pledge week. But modern state and municipal governments are complex institutions collectively spending trillions of dollars every year. Politicians have to learn the boring grunt work parts of being in government, like who does what, how to check the power of the executive branch, how to invest in local institutions, and what interns they can trust with their naughty pictures.
The subtle intricacies take years to master. Were you better at your job when you just started, or after you had five years of experience? But term limits prevent politicians from developing that experience, assuming they even bother trying in the first place, knowing that they'll soon be looking for a new job in a different field anyway.
But you know what job doesn't have term limits? Lobbying. Lobbyists have mountains of research, money, and connections, and they know how to craft laws to get what they want. An inexperienced politician is easy to influence, for the same reason that a shady mechanic can screw you if you have no idea how a car works. This also means that when popular laws and programs lose the people who crafted them, they're more likely to crash and burn. The new class doesn't know how to update them to fit changing circumstances.
In fact, a great way to make money after hitting a term limit is to go into lobbying. People with the skills to get elected can use those skills to summon oceans of cash once they've left office, and no longer give a shit about the concerns of anyone but Big Arsenic, or whoever else is funding the payroll.