With Bitcoin, it works because of the joinable UTXO's , like this:
Generate a key pair for each customer, and associate the public address with the customer id.
Receive payments from multiple customers, simply identified by the addresses.
Periodically spend the total amount to offline wallet, with a single transaction.
You can accumulate hundreds of payments in a simple and economical way.
How to implement this with Ethereum?
Note: identifying customers by their sending address is not an option for multiple reasons.
Note: if the answer is resolved to be "It's not feasible", the follow-up question would be, "What is the best alternative?".