To borrow from Will's argument you already do when the transactions you don't propagate are confirmed. I am not against side-channels I just don't know what happens if a company pays a premium to a miner for inclusion and another miner snags it from propagation (because why just bet on one horse). Do they get a fee refund or is that a cost of doing business?

Direct to miner solutions prevent those tx's from being gossiped to avoid this.