It sounds like there may be some design flaws in their navigation protocols or automated systems.

When in busy international shipping lanes you are going to be spotted visually and on radar by other ships, including ones from countries that cooperate with those unfriendly powers you want to avoid. Your general position is going to get back to those unfriendly powers.

So is there any point in turning off your transponder when in such waters? It seems from my inexpert viewpoint that if you are running with your transponder off, you should also be keeping out of visual and radar range of other ships.

Sure, if the transponder is off so that the unfriendly power is only able to track via reports from friendly (to them) ships, there will be some delay in their tracking. The unfriendly power won't be able to launch a long range cruise missile attack on you based on such tracking, but that's only relevant when you are in an active conflict with someone who has that capability. The US currently is not. The unfriendly powers currently interested in US navy ship positions only need to know the general area of the ship to figure out the things they are trying to figure out.