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Using ECDSA, given a signature and the message signed, it is possible to recover the public key. So it seems to be a waste of up to 65 bytes in each transaction. Why does bitcoin do it? Which cryptocurrencies use the key recovery approach?

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it is possible to recover the public key

Yes. But this operation is slow (comparing with other bitcoin script operations). May be Satoshi Nakamoto did not know about it. Anyway, the hard-fork required to implement it. So, you are welcome to create hard-fork or altcoin with this feature implemented.

Have a look to this discussion: https://bitcointalk.org/index.php?topic=6430.0 I can not explain better

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