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No, with error correction, not all transmitted bits are received, but the message bits can be recovered.., and if not they must retransmit later.

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I meant the message bits carried by the emission, but you're right, the way things are done, more bits are prepared at first, to make the message more resilient against noise, and only then all the bits are modulated onto the EM emission. So while not all emitted bits do come correctly, all data bits can be reconstructed.

Which makes me wonder, whether this way of achieving resilience against changes along the way is necessary. Maybe the data bits can be modulated directly onto analog current, and error resilience can be achieved by remodulating it on the analog level. Then, the emission would have as many bits as there are in the message, error-resilience (modulating, demodulating) would be done strictly using analog electric circuits.

By adding additional degrees of freedom in the transmission through 'analog modulation' you increase the transmission rate. This is certainly possible, for example FM is more robust than AM, but at the expense of bandwidth. In the presence of a thermal (Gaussian) limited noise model, the Shannon capacity always applies regardless of the modulation.

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