How often do you see a Scrum Team with its own dedicated Scrum Master? While this is the recommendation, I bet you've seen more of the following.
Dual Team: The industry standard is 1 Scrum Master serving 2 Scrum Teams.
Dual Hat: Common enough variant of lessened dedication where one person wears 'two hats'... one of the Scrum Master role, and one of an individual contributor (analyst, tester, developer, ...).
Rotating Hat: Less common variant of lessened dedication where one person wears the Scrum Master role 'hat' for a Sprint, and then the 'hat' is passed on to somebody else the next Sprint.
This is based on fear.
I'm not saying it's a bad thing... I'm stating my opinion of where the organization likely is, and this has to be accepted if coaching is to be effective. If the organization was fully bought in to the power of Scrum, then they'd fully invest in Scrum for their teams, and this includes 1 Scrum Master per Scrum team - by definition, if you're saying you're playing the Scrum game.
I'm also not saying you can't do a lot of Agile good in having some Scrum Mastery in a team, especially versus none... I'm suggesting that you're significantly reducing the potential of the role. Time to make my case. Let's start with some of what I've blogged here about the role.
pay attention to the team and the environment through the lens of servant leadership
help everyone understand Scrum theory, practices, rules, and values
"new process experiments over time" as the meta-metric uniquely aligned with the Scrum Master role