Dante encountered more than a few F-rank monsters on his way and dispatched them. He wouldn't arrogantly claim that he was too big for them or that they would waste his time.
A person with devouring talent would be a fool to let go of anything that could increase their power unless it literally brought no numerical increase to their power. Dante knew that many behaved this way due to laziness, feeling that these small morsels were not worth the effort.
Well, he didn't particularly mind anyway. The more of them he killed, the higher his payout score at the end of the 30-day period. Not to mention, all the F-rank Mutation Cores could either be sold for money or traded for higher-level Mutation Cores from those in need.