That's a very strange definition for "just fine." A submerged submarine cannot function without moving, especially if it is altering its buoyancy radically by firing torpedoes. Having a solution that is only momentarily valid is also not "just fine."
Since you can do constant bearing attacks without using the TDC at all, and the above defined "just fine" TDC gives you no advantage over the constant bearing attacks, "just fine" is extended to a submarine with no TDC at all!
A TDC is on a submarine to provide additional alternatives which would not be available without it. Tracking your boat's motion opens up a whole constellation of possibilities for sinking targets which might remain untouched otherwise. The position keeper, able to predict future positions of the target without future observations does even more to extend the deadliness of the American submarine. Not having those capabilities is not "just fine."
By the way, the German TDC had the same automatic input for ownship course. Otherwise it could not calculate a gyro angle at all. After all, gyro angle is calculated from your heading. No heading info--no gyro angle. You cannot escape that requirement.
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