By "operator pushdown", i mean any ability to filter or map over the contents of the object on the server side in some way, sending only the results over the network to the client.
For example, say you have a huge CSV file of customer orders in a bucket. You might want to find the timestamp of all the orders which included a particular product. If all you can do is stream the whole file, then you need to do that, just to pick out a few timestamps. But you could imagine a kind of request where you say "only give me lines where the product ID is P01234, and only send the timestamp column". Perhaps you would express that as a pair of regular expressions, or a sed program, or a Lua script, or maybe the server would understand CSV and let you write something a bit like SQL. There are all sorts of ways it could be done. Providing a fully general way might be tricky, but it wouldn't need to be fully general to be useful.
I appreciate that if you want to do this sort of access frequently, you should probably be using a database, not object storage. But it seems like a very useful feature to layer on top of object storage, and one that feels like it should be fairly cheap to execute - the server has to do a small extra amount of computation, but then needs a lto less network bandwidth.