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
Let me add a few aspects of the role that are relevant to this discussion.
impartiality & objectivity
depth of team coaching
Alright. The bulleted list items are my ingredients. Let's see what we can cook up.
paying attention: wearing the hat with split attention and limited time lessens the ability to empathize with the role, and really get what servant leadership can feel like: the change in stance, and the level of responsibility you feel to your team mates
help understand: everybody's understanding of Scrum will be different, which means the implementation of the framework will be inconsistent at best, harmful at worst, thus the lack of consistent guidance significantly reduces the alignment of understanding, and consequently the success of the Scrum implementation
meta-metric: while anybody can come up with a process experiment, follow-through and the regularity of this practice are where a lot of the value lies, where inconsistent role ownership can result in inconsistent benefits from Kaizen
impartiality & objectivity: these require somewhat of an outsider's stance, which can't be faithfully exhibited if the team member goes back into regular team involvement at the end of a Sprint
coaching depth: mastery takes time and focus, and hat rotation does not allow for the hat wearer to focus on the team long enough for meaningful impact
paying attention: alrighty, hat permanence begets consistent attention, albeit split attention here, as the tasks of the individual contributor role are balanced with that of Scrum Mastery
help understand: hat permanence also begets consistent guidance, albeit lesser guidance here, since the hat wearer is also individually contributing through the Sprint
meta-metric: there's now a better chance at follow-through with, and regularity of, new process experiments over time, since there is now someone to focus on Kaizen over time
impartiality & objectivity: good luck holding a neutral stance when you're also involved
coaching depth: while the presence of coaching may now be more consistent over time, it is difficult to lean into the role in addressing the whole team if you are also part of the team
paying attention: sure, you guessed it, greater paying of attention if you don't also have to balance individually contributing, and this case is the industry standard
help understand: greater guidance here than the previous case
meta-metric: if all the Scrum Master is doing is coaching at a team level, then she is likely to notice more nuance with the Kaizen we are trying
impartiality & objectivity: finally
coaching depth: well now you can fully take on the persona, fully leaning into the role of coach, and not feeling held back by any conflicts of interest when compared to the previous case
Now let's cover the case where the organization fully invests in Scrum for their teams.
One Hat & One Team
paying attention: just one team to focus on (I've had up to four) of course means you will notice more... more of the team's individuals, team's dynamics, and the environment
help understand: better knowing the team and its members builds trust, which can foster greater understanding
meta-metric: expect more Kaizen nuance not just when running the experiment, but also crafting it, since it can be better tailored
impartiality & objectivity: check
coaching depth: the reality is one team will get the majority of your focus at a time if you have more than one to coach, thus slowing the momentum of coaching for those minority teams... so having just one team to coach better guarantees consistent momentum with a team's evolution
So if you're saying you don't need a dedicated Scrum Master, then fine - I don't know you :) , and I don't know what you need; however, when you say stuff like that, you should know on what you're missing out. You're significantly reducing the potential of the role. You're not fully investing in Scrum for your teams. Your not doing Scrum is based on fear.
And that's OK.
That's where you are.