Why Adaboost SAMME needs f to be estimable?
Think for a while, if $f$ is not estimable, it can have any constant added to it with no difference on the result of the process.
This means that if no other constraints are imposed, $f$ is not well/uniquely defined and in fact represents a whole class of functionals. This obviously needs to be fixed and some natural constraint needs to be added (to uniquely fix $f$).
On the other hand, the additional constraint can also be seen as a free parameter of the process which nevertheless needs to be fixed somehow in a concrete instance of the process in order to take place.
In an analogy with physics, the algorithm is &quot;gauge-invariant&quot;, but for any concrete physical problem to be solved some &quot;gauge&quot; needs to be chosen and fixed.
They choose to impose the symmetric constraint which reduces to the usual AdaBoost in the 2-class case.
One can impose another constraint on $f$ (than the symmetric one), choosing to satisfy other criteria if so desirable (as long as it can uniquely fix $f$).
For example, the general non-symmetric constraint is also valid:
$$f_1 + \dots + f_K = c$$
for arbitrary constant $c$. This also fixes $f$ uniquely and it can introduce bias favoring certain classes over others (eg for an imbalanced problem). Additionaly, unless $c=0$, does not reduce to the (symmetric) AdaBoost in 2-classes case (which may or may not be desirable).