To be fair, there's a difference between long-term storage and working memory. The magnetic-core memory you're talking about is RAM, not storage. Though it is looking like the two may converge some time in the future, until now "working memory" (RAM) in computers has always been far lower-density than storage, but far faster, for use in computations (and also volatile, unlike storage which is non-volatile). It's the equivalent of comparing your brain's short-term memory (when thinking about a problem) to your hand-written notes. Punch cards are indeed the appropriate comparison.
But to get back to your original point, a washing-machine-sized storage machine is perfectly acceptable if that's all your technology allows. In fact, it'd even be acceptable now, if it allowed you to replace what currently takes a whole data center's worth of hard drives. I'm sure Google would be ecstatic if they could store all of YouTube on a single machine the size of a washing machine.
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To be fair, there's a difference between long-term storage and working memory. The magnetic-core memory you're talking about is RAM, not storage. Though it is looking like the two may converge some time in the future, until now "working memory" (RAM) in computers has always been far lower-density than storage, but far faster, for use in computations (and also volatile, unlike storage which is non-volatile). It's the equivalent of comparing your brain's short-term memory (when thinking about a problem) to your hand-written notes. Punch cards are indeed the appropriate comparison.
But to get back to your original point, a washing-machine-sized storage machine is perfectly acceptable if that's all your technology allows. In fact, it'd even be acceptable now, if it allowed you to replace what currently takes a whole data center's worth of hard drives. I'm sure Google would be ecstatic if they could store all of YouTube on a single machine the size of a washing machine.