First, to clarify again, the question is about one-time addresses, i.e. stealth addresses, which are different than the public addresses. The public addresses can be reused freely, whereas the stealth addresses cannot. For consistency, I'll only use the term stealth address (one-time address) in this answer.
To answer your question, we first need a bit of background. In Monero, key images prevent double spending in the blockchain. Key images are generated by the receiver (Bob) of a transaction, to see if the outputs that belong to him are spendable. Or to put differently, if they aren't already spent. The receiver wants to verify this, because he will most likely want to spend his funds somewhere in the future. From core-team member luigi1111's article:To check if P is spent, Bob computes its "key image" and queries the blockchain to see if it is marked as spent. Key image I = xHp(P).
Note that P is Bob's stealth address, with P = Hs(rA)G + B.
Where:P -- the final stealth address (one-time output key, the destination where funds will actually be sent); Hs* -- a hashing algorithm that returns a scalar (i.e., the hash output is interpreted as an integer and reduced modulo l); r -- the new random scalar Alice chose for this transaction; A -- Bob's public view key; G -- the standard Ed25519 base point; B -- Bob's public spend key.
From the formulas we can infer that, if the sender (Alice) uses the same stealth address of the receiver (Bob) for two transactions, Bob's outputs of one of the transactions will be burned. That is, both transactions will generate the same key image for Bob. Therefore, only Bob's outputs of one of the transactions are subsequently spendable. Now back to your question, given that stealth addresses are randomly generated, is it highly unlikely that Alice received the funds she has subsequently sent to Bob on a reused stealth address as well. Therefore, the key images generated by Alice are unique and...