Popularity based mining (variable block reward) I am thinking of an alternative mining scheme where block reward would grow (or decrease) with popularity of the coin. The rationale behind this idea is to make an exchange rate more stable since greater interest will not result in higher coin price.

The biggest question is probably how to technically solve such variable block reward because there seems to be no easy way of how to collectively decide on reward height.
How would you define popularity? Any measure you make must be decentralised, and whatever you decide on can be arbitrarily faked. It's completely impossible in the terms of a trustless currency like Bitcoin.