Card advantage is very, very important in most card games. It's more important in Magic than in The Spoils, but it's still one of the most important facets of a Spoils game. The Spoils just allows us to quantify it better. A card in hand is worth approximately 3 resources (the cost to draw a card using the faction's draw ability). With a card like Free Trade Agreement, you can let each player draw two cards. When you do, you give each player the equivalent of a net gain of 6 resource points. That's a balance that works much like your howling mine example. Anesthetizing Oppulence, however, costs you 7 (4 + 3 for a card). If you kill, for example, a Plodding Brute, you spend 7 and they only lose 4 (the cost of the brute), because they get the cost of the card recouped.
Fundamentally, removal doesn't win games, it just allows you to ply a winning strategy in the absence of a threat. A card like Irresistable Bribe gives them influence, certainly, but, used properly, it opens them up for more influence loss than they gain from the bribe. I would always rather give my opponent influence than a card, particularly in exchange for a known threat.
The Gnomish One: Cracking Heist Planners in sealed since 2006.
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The Garbageman can because he mixes it with love and makes the world smell goooood.