The problem isn't the camera, it's the uplink to Perseverance and all the other parts required for a usable camera. They're using Zigbee [1] to communicate with the Rover at 200 kbps and the solar panel recharging the batteries also have to power heaters to keep the electronics alive - there's no hardware connection between the two for data or power exchange AFAICT. The drone is already so heavy that it can only stay aloft for 90 seconds to a few minutes between charges so between the extra battery, lens, better antenna and RF module, etc. it'd require a redesign of the entire mission.
It's not that heavy, relatively speaking, it has to spin the rotors a lot faster to gain altitude in 1% atmosphere of Earth, hence the shorter flight time.
The Snapdragon CPU has plenty of power for JPEG encoding and likely even hardware accelerated encoders. The 640x480 8bpp navcam images could be entirely usable at a fairly lossy 40:1 compression ratio which ends up about about 8KB per frame, for a 90s flight recording at 10fps that's only about 7.2MB to record the whole flight. It would take a little under 5 minutes to send that back to the rover at 200kbps. The color high resolution camera isn't set up for high frame rate recording IIRC so that was never an option.
High quality 30fps video was never really an option but it's entirely possible/likely to get navcam video after a flight. The Snapdragon is also fast enough to do intraframe compression codec (even h.264) for the navcam video to be able to stream it live back to the rover for relaying back to Earth later like was done with the landing imagery.
The nature of Perseverance relaying through orbiters for high speed uplink to Earth was always going to preclude "live" video from any instrument. The only data important enough for "live" transmission is vehicle telemetry and even then that's only available for the portion of a sol (Martian sidereal day) that Earth is visible from the rover.
[1] https://rotorcraft.arc.nasa.gov/Publications/files/Balaram_A... - page 15