They do, but these maps are either incomplete, or they don't always follow them.
The Los Angeles-class nuclear submarine USS San Francisco (SSN-711) nearly sank on January 8, 2005, when it hit an uncharted undersea mountain about 364 nautical miles (675 km) southeast of Guam while operating at flank (maximum) speed at a depth of 525 feet (160 m). [1]
The Seawolf-class nuclear powered fast attack submarine USS Connecticut (SSN-22) suffered damage on October 2, 2021, after it collided with an undersea mountain while maneuvering in the South China Sea. [2]
And the Swiftsure-class nuclear powered fast attack submarine HMS Superb (S109) had to be decommissioned ahead of schedule due to the damage it suffered during a collision with an underwater pinnacle in the Red Sea, 80 miles (130 km) south of the Suez Canal. [3]
Makes you wonder why they don't have forward-facing sonar as standard during non-secret ops. I mean, there's not a whole lot of shifty things you can be doing off Guam, if you already own the place.
The position of most submarines at any given point is considered actually secret, especially if it is underwater.
Great expense is undertaken to monitor and listen for other countries undersea vehicles as well.
* forward-facing sonar is always being used at all times while a submarine is underway
* however, the sonar that's always used is passive, and since mountains don't move, passive sonar doesn't find them
* active sonar could theoretically be used, but the risk of communicating a submarine's position relative to the chance that you'd hit an underwater mountain is balanced strongly on the side of running silent.
There's always training as a good excuse for running silent. Apart from that ... well, I'm not quite sure what these fast attack submarines are doing out and about at all. Maybe looking for other subs in the area? But whatever they are doing probably benefits from being hard to detect. If you are comfortable with announcing yourself with active sonar and are not just on the way to somewhere else, why not just use a surface ship in the first place?
What do you think would be easier: tracking a sub when you have tons of data linking your clandestine sensors' information to their location as broadcast by sonar, or when you don't?
Yes- the US has maps with higher-resolution data on water depth around the world than what's commercially available.
No - those maps aren't perfect. Some areas are extraordinarily well-mapped, others are less so.
Submarine crews are trained not to check just the charts that are in use for a particular voyage, but also other charts covering the same area. (The USS San Francisco collision has no evidence of a seamount on the charts in use, but there was "discoloration" on another chart covering the same area.)
Jonesy: "Sir, remember the dispatch we got about Russian sub skippers running the Canis ridge at high speed because they had hyper accurate surveys of the underwater canyons?