Why not? Some of the most iconic physical card games have had aggro or burn decks that more or less work this way & those games are still quite popular. I don't see why Hearthstone should function differently than the working genre of gaming.
People are trying their hardest to take out every aspect of rng from the game because they don't like it. Fact is what you draw in a game is always going to determine how well you play a game out, to one degree or another, because card games are supposed to be centered on random drawing to a large margin. Players should be grateful that you even get to mulligan cards at the start considering many more games pretty much stick you with what you first draw. Aggro decks are simply trying to make what you draw as being more consistently useful, bypassing the concept of a bad draw made up of high cost cards.