The depth is deep enough to float almost anything through but there are sections where it is critical to stay in the channel. My first westpac we transited the Strait of Hormuz from the Arabian Sea into the Persian gulf; man does it get narrow. Gave us all the willies. I was the master helmsman so it was stressful.
You could dredge more shipping channels but it would probably take months and a lot of resources.
Surfer