Here's the thing; if the mulligan gives your opponent an advantage, your deck is terrible. That would mean you depend greatly on having your opponent get a bad hand on the first draw. All the mulligan does is improve your chance to draw 0-cost cards. You should be able to handle an opponent with a great hand.
Even aside from that, the only way the mulligan would be bad news for you, would be if you have a ton of 0-cost non-pillar cards which should not really be played on the first turn, like holy flash or sundial. If you center your deck around 0-cost pillarless cards like nova or immolation + photon, the mulligan will work just as well for you.