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In order to get fine detail resolution in the pic, the IFs have to be stagger tuned. And stagger-tuning reduces overall gain. Add another IF stage for more gain, and you can stagger-tune for a wider IF bandpass, allowing finer detail resolution. So more IF stages equals better fine detail in the pic.
(Then into the 1960s, high gain IF tubes were developed (e.g., 6EH7, 6EJ7) which allowed good bandpass with just two IF stages.)
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