This is an excellent question. The Ottoman, Safavid, and Mughal empires all had one important element in common. Each of these empires were largely land-based. That is not to say that they did not have sizeable navies. The Ottoman Empire certainly commanded respect on the water, but the Ottoman Empire controlled land around the Mediterranean Sea. While it certainly could access larger bodies of water, much of their navy was built for combat on the Mediterranean. In addition, Ottoman naval power was incredibly curtailed after Lepanto in 1571. After that, Ottoman power resided primarily in its land forces. The Safavid and Mughal empires, much like the Ottoman Empire, were defined much less by their influence on the seas.
This situation essentially left a power vacuum for those empires who based their power on their seafaring prowess. In the age of exploration that was the sixteenth and seventeenth centuries, sea power proved more important than land power, and it proved less fraught with danger. Controlling the sea routes directly contributed to the success of the seafaring empires.