Going around would take too long and at each end there a huge Chaos empires to deal with, the Eye on the North end and the Scourge Stars at the South. Chaos forces are still pouring out of the Rift raiding and razing everywhere, the Nids are still about, the T'au and Necrons are pushing into Imperial space again. Nihilus is very much a problem but not the biggest one the Imperium has to deal with right now.
What Chaos empires? The one that has existed inside the Eye from before the Great Rift? That these same systems had already put up with for millennia?
You also have to remember that space is massive and, again, omni-directional. It's said that undiscovered alien or human empires could exist in Imperial territory. Even if Chaos lays claim to a specific area of space. There's no way they could patrol all of it.
It also depends on the planet you're talking about. Mordian might prefer to reroute their shipping around the Eye via the safety of the Calixis Sector to Chinchare. Where goods could then be off loaded and then shipped across the safer side of the Imperium and vice-versa.
Obviously if you're a planet like Armageddon, Elysia, etc you'd prefer to secure and go through the Rifts safe passageway in the galactic north.
There are supposed to be systems/realms/empires of chaos but GW
doesn’t talk about them much. I don’t feel like they ever got their act together with joe they wanted to portray chaos in 40K
and they’ve made it all about CSM
and the eye of terror.
Some of the 40K
Belakor fluff states that he controls an enormous empire somewhere win the galaxy but no idea if it’s current.
The blood pact would be another example, not sure if they were part of an empire