We teach be able to as well as can/could. Students need it to talk about future ability. But there are interesting twists in present-time and past-time situations as well.
Requests Versus Ability in Present-Time Situations
When teaching about ability, we cover be able to as well as can/could. Students need it to talk about future ability. But there are interesting twists in present-time and past-time situations as well. One of them involves ambiguity about requests versus ability.
Consider the question, “Can you pass the salt?” It is a simple request—with the word can as a polite distancer. To be even more polite, we use the slightly more distant form could. Neither question about salt concerns what the listener is able to do. What happens when ability is really the issue? That’s when can/could might not be very good choices, even though they are correct.
Some print is so small that I’m unable to make it out. If I ask you “Can you read what it says there?”, my request is ambiguous. Do I wonder whether you can read it, or do I want you to read it for me? If I want to address ability with no misunderstanding, I would use “Are you able to read what it says there?” In this present-time context, if I use could, I must be making a request. The only possible reason for could in a present-time context is for a purpose like distancing. “Could you read what it says there?” will almost always be interpreted as a request.
Talking About the Past
Let’s look at a past-time context. You say, “Dave lived far away and didn’t have a car.” All the rules say that I’m fine in responding, “Could you give him a ride?” I’m almost certainly asking about ability. It would be weird for me to blurt that statement out as a request in that context. However, you may notice that some people are deterred nonetheless. I’m one of them. The mere hint of possible ambiguity with could causes me to prefer, “Were you able to give him a ride?” Am I the only one who feels that way? I don’t think so. I’ve often observed other people in those past-time contexts start with “Could…” and then switch to “Were you able…”
For excellent materials about teaching the grammar of ability, see Grammar and Beyond, Level 2, Unit 19.