"This is not Agile!"

Did you ever argue with a "Scrum Coach" who told you that your Scrum introduction was proceeding too slowly? That solutions you fought hard for were "not agile"? And did you at the same time have the feeling that so many changes were happening at once that you were overrun by them? Or have you been the coach in a transition project and had the feeling that "everything is moving into the wrong direction"?
If this is the case you are in the good company of most people who actively took care of a Scrum introduction.

First, one insight is essential: Neither Agility nor Scrum are ends in themselves. Nobody should try to introduce Scrum just to "have it". That's not the point. Scrum is a tool which helps you to gain transparency and become agile. You only should pursue the goal of Agility if this solves existing problems and improves the whole system at the same time. This means that the purpose of a Scrum introduction is always and without exception the improvement of your organization's ability to compete.
Therefore you have to ensure smoothly running regular operations during a Scrum introduction. This is especially important since such a big change can take months or even years to implement. No company can afford to stay unproductive for so long - and Agility does not just occur over night. As a rule of thumb you can say: The bigger the enterprise, the longer it takes to achieve Agility, as does every single step on this way.
The reason for this high demand of time is that people change slowly. This is a good thing! Imagine a world where every human being fundamentally changes his attitude every five minutes. Chaos would reach a degree most of us shouldn't want to strive for... The same is true for organizations: These systems are usually in an equilibrium that is disturbed by the introduction of agile methods. Now it is important to retain a sufficient amount of stability while allowing some evolution at the same time. Thus there is nothing else for it but to accept the slow speed of change and to adapt to it. Change never happens against the people concerned - it can only be successful together with people. This leads to two conclusions:

We have to make sure people involved in the change do not panic. Everybody will have to leave her comfort zone and move on into the "learning zone". The "panic zone" is then just a tiny step away and must be avoided since panicking people no longer think rationally and are not able to see or even value the positive aspects of this change.
The affected parties must generate successes and realize that they are successful indeed in order to keep their spirits up.
You only have a chance to successfully introduce Scrum and influence the organization's culture positively if both aspects are fulfilled.
"Hybrid approaches" - mixes of traditional and agile processes or ways of thinking - can help to pick people up where they are and take them along while not overstraining them. In practice this means that such hybrids are okay as long as they help the organization and are seen as an intermediate solution on the path to Agility. The introduction of agile methods is a journey - every step into the right direction helps, it doesn't always have to be a quantum leap. Agile Coaches must be aware of this. View the coach as some sort of midwife: She supports the mother-to-be with farsightedness and experience to give birth to her child. But the midwife does not have to go through the pain herself. Demanding to "finish pregnancy faster" or "get the child out quicker" does not help, no matter how fervently it is stated.