Shor's integer factorization algorithm needs a single number or key to factor, not hundreds of transactions. I've certainly sent money to old addresses, which exist in perpetuity on the blockchain. I can also use web searches to find hundreds of current public keys in a matter of minutes.

> currently Shor's algorithm is unfeasible with only 1 signed message.

The algorithm is currently unfeasible with 100s of messages. Shor's algorithm uses a quantum computer to reduce the complexity of integer factorization from sub-exponential to polynomial-time. It is not an attack that fine-tunes the output according to the amount of network traffic.