The tether is not connected directly, it's connected to a TMS that then has a smaller cable connected to the submersible.

Ex.

https://www.researchgate.net/figure/Schematic-image-of-a-wor...

https://f-e-t.com/subsea/vehicles/tether-management-systems/

There's also this one which looks like it can get to the depths of the Titanic:

https://nautiluslive.org/tech/rov-argus

So it was certainly possible to do this with a tether, but it would have been much more expensive.