Ok, please be aware that i'm just playing around here; thinking loudly. Tis is not to be taken too seriously and not aimed at a specific usecase now, but could evolve in that direction.

What if the token can also be seen as a negative thing? Holding a token would be an obligation, not an advantage. A possible scenario could be like this:

The tokens are auctioned off as described, but it's a negative auction: users pay fees not to get the token.

For every block or number of blocks, a token is sent to the account which paid the smallest fees.