Post-board you should replace them with Extirpate
If you can't draw a card at the start of your turn because your library is empty, you lose immediately
The classic cards to dish out with a Harmless Offering are cards that are bad to control
A different example of this would be that I rate Lightning Helix as a very powerful card but only as a fairly average burn spell
The value is there
Those cards are: Essence of Orthodoxy, Seedpod Caretaker, Phyrexian Pegasus, Interdisciplinary Mascot, Referee Squad, Zephyr Winder, Terror of Towashi, Seer of Stolen Sight, Injector Crocodile, Orthion, Hero of Lavabrink, Axgard Artisan, Cragsmasher Yeti, Surrak and Goreclaw, Ruins Recluse, and Fairgrounds Trumpeter.