My position on wallets regardless of being offline, cold, or online is that once the private key has been used to move any coin, you need to move the remaining balance to a new unused wallet address and not re-use the source address again. In other words, wallets are theoretically safe indefinitely, but any wallet address that has been used to move even 1 Satoshi out needs to be abandoned and never re-used again. Wallet addresses used for out bound transactions are therefore temporary. If you don't keep a balance in a given wallet, then theoretically, you may be able to safely re-use that address assuming no balance is kept for any length of time (i.e. you sweep accumulated balances to another address frequently).
I'd like someone from this forum to challenge or confirm the premise with backed up logic.
Can you explain why a wallet should only be used once and not re-used?
He doesn't say that "a wallet should only be used once and not re-used". He says that "you need to . . . not re-use the source address again".
A wallet can have multiple addresses. As long as you use a new address for every transaction (as suggested in the original Satoshi Whitepaper, and by many knowledgeable experts), and a wallet that generates new addresses for "change" (such as Bitcoin-Qt) you can re-use the wallet as muh as you like and will have all the security that the OP is suggesting.