This is about a revolving door programme of hiring coaches. One of the things I’ve observed regularly, is that these kinds of hiring programmes create an implicit timeframe by which improvements must be “delivered”. In itself, that’s not necessarily a problem. What is a problem, is that the timeframes are nowhere near long enough (IMHO) if the aim is to change the culture.
How you measure your coaches also has an obvious effect on your outcomes. Procurement plays a big part here. I’ve seen a lot of coaches who have their success defined by some variation of how much effort they expend. Training courses run. Numbers of teams “coached”. Amount of collateral documented in a wiki/repository/etc. It’s even worse if that’s also what the coach genuinely believes is a measure of success.

It’s easy to buy the visible stuff. However, the visible stuff has no sustaining ability – that comes from the hidden stuff. Agile’s a culture, but how do you buy a culture? It’s much easier to buy a new set of processes, dress code, office layout, stationery, reporting templates etc.
By buying the visible stuff, you easily get to a set “maturity” of what-to-do (because your coach has implemented this a million times), but you might lose the learning-about-why and your ability to improve at some point comes to a crashing halt when your coach runs out of instructions to give you (or they leave). You’ve substituted thinking for doing what you’re told because an expert tells you.
One of the things that could lessen the likelihood of this happening to you is longevity. Although that does bring its own set of challenges. Longevity can come from humans, or guidance that’s respected enough to be followed (or at least attempted) – e.g. the guided continuous improvement advice from Disciplined Agile Delivery’s collateral.
Longevity can increase the chances that the underlying factors get some attention – beliefs, culture, mindset. But longevity is hard. When things go wrong (and lets face it, things always go wrong), it’s easy to blame the changes that are being attempted. I’ve often seen blame being thrown about as a precursor to the environment becoming more toxic. In those environments, unless there’s sufficient emotional investment, coaches leave.
In my view, the most effective counteracting force against that toxicity, is leadership. Your senior leadership must have the trust of the members of the organisation. However, trust doesn’t come from great speeches but from credibility. That means the senior leadership must also evolve and adopt a more collaborative/open/trusting/etc culture. They must behave differently. And they also need to provide regular, ongoing and consistent reassurance that the environment is safe so that teams can evolve to a more agile culture with no repercussions for steps that don’t quite make it on the first try. I think that works because humans emulate leaders. If the leaders are open and collaborative, then the teams are more likely to also become more open and collaborative.