There are several companies will only offer customer support over phone. Often times ending with: "We put a note in your file and sorry but the computer doesn't allow me to send you a conformation of this call." Are US based companies required to send you a conformation that the call occurred with the result of it?
No. In general, a business is not required to provide proof of interaction with a customer, though if you sue them for breach of contract because they failed to do something they are required to do, they would need to provide the proof to the court that they actually did it, if that is their claim. It is always possible that there is some contractual obligation to send confirmation, e.g. a clause that says "If you request service under clause 7, we must provide written acknowledgment of the request within 48 hours"; you can certainly request such a condition in a contract before you sign up.
Computer confirmation, or indeed written (surface-mailed) confirmation is never necessary, but some proof of having made a request may be necessary. For instance if the contract says "Customer must notify Service of this problem within 14 days of Event". One way to handle this is to submit your notification by certified mail, though that is not free of problems (if you have no idea where to mail it to). Another is to record the call: however, in some states (the "all party consent" states, such as Washington), you can get in trouble for doing this without notifying the other party (solution: announce that the call is being recorded). They may say something like "company rules do not allow you to record calls with us", but that is nonsense, and you can insist that you will record the call (they then may elect to terminate the call).
A third option, not as effective from the evidentiary perspective, is to have a witness present in the room. The wording of the all-party wiretapping laws might prohibit using the speaker without consent from all parties, but no law prohibits a third party from hearing your end of the conversation and testifying that he heard you say such-and-such. You can even record yourself talking, without getting the other party's responses (then the question in court would be whether the recording represents half of a real conversation, or something staged by you).