Hence the importance of distributing your coins across several addresses and discarding an address after the first transaction
Not reusing an address? Sure.
Discarding an address? Nope.
I still have copies of every private key for every address I've ever used, even ones which I used once years ago and have never and will never use again. Why discard them? The files/back ups already exist so it takes no effort on my part to keep them, and there is always the chance that I accidentally reuse an address or a third party accidentally pays me to an old address, at which point those coins would be lost forever had I discarded those keys.
In the words of Satoshi:
Sigh... why delete a wallet instead of moving it aside and keeping the old copy just in case? You should never delete a wallet.
I didn't mean throwing them away, discarding an address after one transaction means never using that address again, especially for large amounts, actually reusing an address for small amounts is more convenient. Ordinary people have nothing to worry about. Using the term "discarding" was a bad choice of words.