The value of seeing agile done properly first is significant:

Better understanding. It makes it easier to understand the underlying mechanics when explaining them later.

Achieve quick wins. It shows the team how delivery can immediately be better just by using the right principles and techniques. The coach accompanies the team a couple of times through the process until the team is comfortable enough. It is then time for the coach to step back and let the team apply what they learned. The coach will take on a guiding and supporting role rather than a leading one.

Provide a benchmark. And it provides the team with a benchmark of good agile practices. We see it happen too regularly that teams settle for mediocre agile when they don't have anything to benchmark it against. Although usually still better than what they had before, it is far from the agile performance they could achieve.

A good coach knows which battles to pick

What about letting them decide and fail so they can learn for themselves? Wouldn't that be better in the long run? Absolutely. But a coach should know what battles to pick and when letting the team fail is the best way to teach. Forcing the team to learn everything through failure (versus by example) is often not the right approach. It will likely take too long and make them write agile off as too painful and not a solution to their problem. Not because it doesn't work but because they never had a chance to experience how it could work.

An agile coach is about delivery. About teaching a team how to be successful, to know what 'good or great or proper' could look like. And about making the team think for themselves, to be independent. The best agile coaches we have seen have a combination of real delivery experience, leadership and coaching skills. They know when to do it themselves and when to step back and just coach. The ultimate goal should always be that the team learns through successful delivery.

So the definition of 'agile coach' depends on the stage of maturity the team is in. Purely advising and 'talking agile' is not as effective at improving a team as delivery leadership can be. And what if the agile coach has read all the books and knows all the theory about it but couldn't deliver the project themselves? Well, then they have no business in coaching others how to do it. After all, agile is about practice and not theory.