Requiring a permit to cross the bridge was bad writing, change my mind.

[Cleretic]

That seems like a bit of a contradiction
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It’s the most important bridge in the world so we have to shut it down when the government is having internal issues

They didn't shut it down, they just shut down new permits to cross it. People who already have them can and do cross, we see a handful of them both in the MSQ and sidequests. Reasonably speaking, everyone who has business regularly crossing already had their permits; there's no writing suggesting a huge backlog or great supply/transport issues, we're the only person who really seems to need a permit without already having one, and that's only barely.

Hell, I'd reasonably argue that permits probably haven't been paused for long, because Pashenine in the Fisher questline is unambiguously from Xak Tural, and is quite young. New permits were probably only paused for a couple weeks to a month or so.

Also, there's a yellow quest that briefly goes into the requirements as to why this whole system is needed; Waiting One's Turn, in Shaaloani. It's not fancy reasons; it's just that it's a big, singular bridge with a lot of transport on it, that calls for inspections and permits to ensure that everyone's getting across in an orderly manner with the goods they say they have. Given that exact bridge route both got exploited in the MSQ, and outright attacked in the role quest capstone, yes you do need all that overhead, and frankly there's a case to be made that it should be even stricter!