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.
No good for pulling it to the surface, of course, but reliable communication alone would be a great benefit.
[1] https://en.wikipedia.org/wiki/Nereus_(underwater_vehicle)
https://en.wikipedia.org/wiki/Jason_(ROV)
And the Titanic was discovered by camera sled being towed by a ship.
https://en.wikipedia.org/wiki/Argo_(ROV)
So your search might have been a bit too quick. It certainly is possible possible to build a tethered crewed submersible, though this vehicle wasn't.
Credit to js2 from this comment: https://news.ycombinator.com/item?id=36396161
This sub has 4 Innerspace 1002 thrusters that make for a max total of 342*4=1,368lb of thrust... I think a useful point of reference in deciding how much pull force would be needed for an emergency recovery tether.
I think it's reasonable that a 4mm dyneema line with a breaking strength of 4,000lbs would be sufficient for emergency surfacing, and safely provide much more thrust that it's own motors. The whole sub weighs 23k lbs and is approximately neutrally buoyant.
Total weight for 3 miles of 4mm dyneema is only about 120lbs, and for simple emergency use, in the spirit of OceanGates now infamous "scrappy thriftiness" could be pulled with the type of simple/cheap hydraulic winches used for pulling crab pots, anchors, or fishing nets. 3 miles of this line would have cost about $15,000.
Aside from the massive tether and engine that would need to pull it, I'd imagine it would rip the submersible to shreds at those depths