Watching this video of Perserverance being tested on Earth, it occurred to me that requiring it to stand, drive, climb, etc. under 1g is, in some sense, overkill. Could this (or other) rovers be made more capable or less massy if it was not required to support itself on Earth at all? Has this ever been considered?
The video shows only tests within the clean room on smooth clean test floors. The vibration test at first should simulate the conditions during launch.
Drive tests on a simulated Martian rough and dirty surface on Earth (see JPL Mars Yard) are not done with the version built for the Mars surface. The flight-ready version is built in a clean room and only leaves it to be transported to the launchpad.
For drive tests on Earth, special test versions are built. A drive test version is built without a Radioisotope Thermoelectric Generator and not with the full set of scientific equipment. So, a lot of the mass of the Mars rover is not there for the 1-g tests.
The structure of the rover needs some factor of safety to survive the launch at several g as well as the entry to the Martian atmosphere, the parachute unfolding and the landing with the sky crane. Driving on Mars probably induces far from the highest structural loads the rover needs to endure.
Faster? No. The speeds of all Mars rovers so far have been limited by the navigation software or the available electrical power, not by physical capability. Spirit and Opportunity were both physically capable of driving more than 2000 meters per day, but rarely actually traveled more than 60. Curiosity is capable of moving 2200 meters per day, but can only navigate at 200 meters per day.
Lighter? Maybe a little, but not much. Most of the mass goes into non-structural elements such as batteries, solar panels, and instruments, structural elements where the major stresses don't come from gravity (instrument arms), or structural elements where gravity can be compensated for during testing (wheels and suspension). About the only thing that needs to carry Earth gravity at all times during testing is the body of the rover.