Sure, they can charge an import duty every time you bring your sword into town. The question is, should they? I'd approach that question from two standpoints: What makes for the best game and what makes the most sense?
For what makes the best game, taxation rarely seems fun to me. Sure, if the players are being merchants or running their own businesses or whatnot, maybe you have to include some. And if the PCs are landed, having them pay fees to their lieges literally comes with the territory (and can sometimes be useful in motivating adventures, especially if the territory is having a bad year). But its easy to see how it can be fun to spend money to buy a big house and to store your artworks in it. I'm not sure where the fun comes from heavy gate taxes or income taxation (unless the idea is that there is an oppressive government in city A, so maybe you should move to city B or overthrow the government of city A (whether peacefully or violently)-- I can see the fun in that. But taxation as shake-down by armed thugs feels different from a routine, "oh, you've got a warhorse? That's an extra 3 gp each way.")
As for what makes sense... sure, if adventurers are common or clearly making vast wealth, the government will want its dime. But I would guess that cities would want powerful hero types with lots of money settling in their walls. It makes the city more secure (although it raises the risk of them trying to seize power), it boosts the city's economy, and it creates future opportunities. (When they die, for example, the city will almost surely take a substantial estate tax.) So I would figure that the city would either forbid them entrance (if it fears overthrow), or more likely not charge them for bringing in their personalty. Maybe if they bring in wagons of stuff it needs taxing, and maybe there's a flat gate fee (although really, is it worth spending game time on fees that are measured in silver or single digits of gold?)
I guess I just don't find taxation very fun as a gaming topic. Sure, in the real world, taxes are the price we pay for a civilized society, to paraphrase Justice Holmes, but they're not a lot of fun. So why deal with them more than necessary in a game, except when the PCs seek out activities that need to deal with taxes for versimilitude (shipping, ownership of noble domains, etc.)? If a PC wants to buy a house in my campaign, I'll charge them some money, think of it for possible plot hooks, and maybe give them an annual maintenance fee for taxes, upkeep, etc., and then be done with it. Why try to take away their fun if they find building a real estate empire fun?