From your explanation it is clear that a manager needs to understand what tool or mix of tools are the most appropriate in order to be effective at motivating in a specific situation. So, I too believe that the skills the manager already has may be good to address some situations, but not all.
A manager needs indeed to develop different motivational tools for different situations arising (variation of situation surrounding the employee), and you cannot use the same motivational few tools for all situations.
What might motivate you as a manager might not motivate another employee. Perceptions differ. Assuming that you know what motivates the other can be a big mistake.
A manager may be strongly people-focused and needs to develop his task-focused tools for effectiveness, to develop optimally as a manager. But this is not enough. Constantly updating your skills is necessary.
Good leadership prevents problems before they escalate/occur and create systems to enhance employees’ performance and potential.
Whether 3 or 4 motivation tools are sufficient to be flexible and cope with the various situations? They are not, in my view as already said, although they can help you in some cases. He can still be effective in some case with just those 3 or 4 tools, but not in general, as the needed tools and skills vary depending on the complexity of the environment (see the interactive solution map in the course for the various available tools). What matters is to understand the context and the people around us and try to find the right mix of tools and skills necessary for them, as you rightly pointed out. And learn what is necessary or what we are lacking in order to be effective in that context.