Independent vehicles can descend to the depths of the Mariana Trench, but it is a more difficult engineering solution for ROV's. Woods Hole Oceanographic sent a hydrid vehicle (can operate completely independent or with a fiber optic cable for communication) to the bottom of the trench a few years ago - the Nereus.
Sending a manned vehicle down to that depth is a huge engineering feat and shows the determination to design and build a vehicle that can withstand the environment and sustain human life at the same time.
ROV's have a limitation with the power cable that controls their maneuvering, the length of the cable (over 8,000 meters) becomes an excessive force on the winch assembly. At times the weight of the cable can be more than it's rated load, without the vehicle at the bitter end.
Could an ROV have done the same exploration ? Deep sea exploration, while very expensive, is still not as costly as space exploration. There are some deep-diving submarines available to wealthy and determined persons. Will Sir Richard Branson eventually branch out from Space Ship 2 to deep sea 'flights' ?
It's amazing the range of James Cameron's interests and skills. Not only is he a brilliant film director, but he's really been a pioneer of science, technology, and engineering, particularly as it relates to ocean expedition. There's so much to be gained from this work, and the lessons around engineering will find their way into numerous industries and applications--of that, I have no doubt.
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