The operation is very expensive; first comes the survey to identify a number of sites; that is followed by figuring out which ones are most likely to yield an ancient wreck; then the order of exploration is determined; then the detailed study of those sites begins. It’s heavily dependent on funding of course, but on the Black Sea in particular it’s also weather-dependent.
Ballard’s team needed money, and have a rare, even unique expertise; they were offered a pile of cash to go find that Turkish fighter plane shot down by Syria last year, and went there to do it.
Ballard found a bunch of ancient wrecks while searching for a modern military wreck for Israel. He looked for and found the Titanic with the money and time left over from his successful search for lost US nuclear subs, then raised money to go back and examine the Titanic in more detail.
I guess it is all up to the choice made .... now they have to live by it. They chose to go after the Turkish fighter jet ... a choice and the consequences that go along with it.