It's a great idea, and I hope it catches on
It's important that the sats are either burned in a conventional way, like an OP_RETURN, or sent to miners *in the future* via anyone-can-spend outputs that are timelocked for a long time
Last time I checked, Thomas's implementation does the long-term lockup, but I'm not sure of the status of the paper.
The reason we can't burn them by giving them *immediately* to today's miners is that the miner could simply advertize a notarization service that says "give me 10 sats and I'll do 'fake notarization' for 1 million sats" where the miner just pays fees to themselves