It doesn't. However the lies the conspiracy tell to cover the truth are powerfully strong in convincing people like yourself.
Actually it does work. Submarines and surface ships have been able to navigate succesfully using this method for many years. If they used maps based on an incorrect model, ships and submarines would be crashing into things on an hourly basis. This does not occur. There are no lies here.
The flat earth theorist lies are powerfully strong enough to compel your deficient logic and knowledge to believe them.
It just appears to work. Just as submarines appear to be capable of achieving all kinds of underwater feats. Of course, submarines are incapable of submerging for long periods of time, if at all in most cases, and when they do submerge, they must rely on their periscope to stay clear of obstacles. The reason these things don't crash is simply because they can see ahead, much like the boats on the surface.
Do you ever get outside? Have you ever read a book? Do you live in a basement? Your lack of general knowledge is astounding.
What evidence do you have that indicates submarines are incapable of submerging for long periods of time?
Are you aware that if a submarine rises to persicope depth in the middle of the Pacific Ocean, they will see absolutely nothing, but water on all fronts? So how could they navigate using a persicope with no points of reference?
Nuclear submarines are able to remain submerged for months. Their only limiting factor is food for the submariners aboard. They can manufacture water and oxyegn while underwater.
Submarines only go to persicope depth when they are in friendly waters, as a submarine becomes very visible at periscope depth. Modern day radar is able to detect a persicope. Hence the submarine will only rise to persicope depth when it knows it is within friendly waters. This is a CRITICALLY important fact about submarines.
How do they know when they are in friendly waters? Through use of dead reckoning based on maps developed from the round earth model.
The US Navy of the cold war would have loved for you to have been the planner for the Russian Navy. You wouldn't have believed any of the capabilities that US submarines possessed, hence you wouldn't have built your own submarines.