Great idea and something medium should consider.
I started a series a while back that was still in draft. Just published it. My view was that membership fee should be used (partly) to reward readers.
Your suggestion is way better! You hit it on the head with $1 per recommend.
It will ensure members are a lot more careful about which posts they recommend.
You have my vote.
Of course the challenge will be how to avoid abuse. Im sure someone will find a way around it for short term massive gain.
A good case study / example is the Steem community.
Its cryptocurrency based, but the principles are broadly the same. Writers are rewarded by putting up great content.
Heres an example of todays trending posts :