How much higher should the coach be?

It pretty much depends on the specific coach.

• Coaches are usually more experienced. In some cases this means that age might have already started to take a toll on the rating.
• There are coaches, who are highly specialized, so that their rating does not really represent the skillset you want to learn from him
• Coach stopped playing actively, in this case you do not really know the true strenght of the coach, because he/she has not exposed to a competitive environment for a longer period of time
• Coach is great in explaining, then his rating might be not the biggest priority
• The task of the main coach is very often not limited to the aspects of chess. A good motivator might be worth the money.

In my case I have had a coach, who was a really good motivator. He persuaded me not to stop with chess, when I was stuck around 1800 (fide) and also created a community of students, who were eagerly interested in improving.

Another coach I had was teaching me knowledge, such as specific endgames and the classics of chess. He had not played for over a decade when we started working together.

I for myself in the role as student had discovered that most important to me was, if the coach was genuinely interested in my advance.

In the role of a coach, I try to pass down my experience as a tournament player, give advice on how to deal with different situations from a psychological perspective. The chess education is obviously a big part of the coaching and there I try to implement my students a certain way of thinking, which helps them to find good moves faster.