“That is when Kennedy called off the promised air support”
I don’t think Kennedy ever had any intention of honoring his promise to provide air support. If he had the carriers would have had orders in place before the invasion to provide it. There were no orders before during or after the invasion to provide cover for the ground attack planes.
You might be right but my understanding is the air cover and air supply were both in place and just about to be started when Kennedy called it off.