They splashed down in the Indian Ocean, not the Gulf of Mexico.

Also noone mentioned submarines, debris can just float and drift around (sometimes even at some depth below the surface).

Starship landed in the Indian Ocean, not the Gulf of Mexico.

I mean, yes [0]. It's probably the main reason SpaceX went to effort to recover [1] all the engines of the previous booster (IFT-4), which landed in accessible, shallow water in the Gulf of Mexico. The Raptor engines hold valuable secrets, particularly to China who are trying to clone a lot of SpaceX things.

The CIA did something very similar to this in the Cold War [2], though they used a boat instead of a submarine.

[0] https://en.wikipedia.org/wiki/Akula-class_submarine#Operatio... ("In August 2012, the news media reported that another Akula-class submarine operated in the Gulf of Mexico purportedly undetected for over a month, sparking controversy within U.S. military and political circles...")

[1] https://old.reddit.com/r/SpaceXLounge/comments/1fvdekt/more_... ("More images from B11 recovery + new info "26 of the Raptors have been recovered but they are trying to get all 33")

[2] https://en.wikipedia.org/wiki/Project_Azorian