Sure, there is less lift... But there is also less drag. So your rotors can go far faster with the same power input - and, roughly, it looks like the power needed to hover (for a craft of a given mass and size) is actually less on mars due to the lower gravity, despite the rotors moving super fast.
I think this is a misconception. Even in water, you cannot provide lift equal to your bodyweight.
It is easier to swim (vs sink) in water because the water gives a large amount of buoyancy.
However, in air and on mars, buoyancy is small enough to be negligible.
FYI, these two things are __directly__ related.
Lift = c0 r v^2 A
Drag = c1 r v^2 A
=> Lift = c0/c1 Drag
You should be able to reason this out too. Think about how you generate lift. The blades spinning have to push something, right? What is it pushing? Then think about drag. What is that dragging against? Is it related to the thing you're also pushing against? I think you know the answer.
Yep. Setting maths and motors aside... it's why helicopters have service ceilings and why no one has built a helicopter that can fly away into the stratosphere.
Just like the mars helicopter cannot fly on earth.