You don't need to spend $5 to get card drops. Here's
the Steam knowledge base article on exactly what restrictions apply to limited account. Note that a limited account doesn't have access to the Steam market but they
can trade the cards to an account that does. Likewise, authenticators are required for instant trades but even without them the trade will go through after a period of time during which the item is held in escrow by Valve. There is no hurry to get these cards to the market for the people selling them.
Additionally, this is not a one time endeavor where someone sets up a 300,000 strong bot farm to earn $9000 once and calls it a day. Thousands of games are being released on Steam each month and a lot of those are being farmed for cards. There are tools being specifically coded to automate as much of the process as possible. Some folks simply cannot understand the scale at which this is happening.
Finally, this is not speculative fiction. You can see all of it happening. You can go to sites that are selling these keys in bulk for next to nothing and buy them. You can go to the Steam market and see the cards selling. You can check profile levels of people who are crafting the badges. Regardless of how many hurdles or restrictions you think are in place, this is still an ongoing process. It's why Valve continuously takes steps to curb it and why developers are trying to find ways to bypass every new restriction.
I mean, even Valve admits in
that Gamasutra article that card farming is one of the problems they're trying to combat and you think this doesn't work in real life?