Ah, you see: ideas are free! (sadly) Didn't know Tendermint chains did that.
That doesn't mean there cannot be two different burning mechanisms.
Some time ago. I investigated whether any real economies burnt their money - apart from online games that hold a tenuous link to reality, and to economics - and discovered the Penn Scrip. This is pre-hegemonic-US-dollar and, astonishingly, didn't collapse - was swallowed up anyway. What they did was burn taxes ie activity - they also only lent money to productive industries, hence not to banks. So, again, this was a money supply measure with a consequent price stability and an allowed inflation rate so long as it was matched by productivity. in the broad sense of productive activity.

The selling ads to burn tokens is narrow and would also rely on human intervention, unless the ads were internal - even then, what mechanism would price the ads? a bidding system? Who would use this? I'd have to think it through, though strikes me as a micro-economic measure rather than macro.

External ads would be more useful but would need some programmatic way to ensure that income is used as intended.

I think before a Hive Improvement Proposal, we need a Hive Improvement Team! A HIT anyone?!