Access control problem in oblivious transfer
OT is typically not used as an application in its own right. In the context of access control, OT limits the number of messages received by B but not which messages. I don't know of any real applications for this (you could talk about a subscription where B has purchased the right to read any $k$ articles, but this is pretty artificial in my opinion).

However, OT is a very important and basic building block used in constructing secure computation protocols. It is used in generic protocols like Yao and GMW, and is often used in specific protocols for things like secure set intersection and others.