覚えたそばから忘れてしまう — how is そばから different from てもすぐ?

'The moment I memorize it, I forget it' — apparently this is the classic example sentence for Verb そばから. Could I just say 「覚えてもすぐ忘れてしまう」instead? Is そばから adding anything beyond speed, like a sense of futility or repetition?
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沐學 Mizuru