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Does this mean that the network becomes more cost-effective to operate as it grows?
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It means that the network is becoming cheaper to attack, basically. Satoshi was working from the assumption that the cost of mining will approach the price of the coins mined. If the TX fees don't increase substantially when block reward is halved, interesting stuff will happen: Hangers full of mining gear will suddenly become unprofitable to mine with -> available dirt-cheap for more creative use, like 51% attack.
Doesn't this seem like fearmongering? In a year, who knows what these charts will be showing..
Worrying about mining being unprofitable in a years time is silly.
We heard the same stuff before the first halving. Miners would stop and the difficulty would be so difficult that it would never adjust, blocks would take years to complete.
It was all true. Bitcoin ended that day. The bears won.