At the end of the Introduction to a recent work of Joël Bellaïche to appear in Inventiones one can read a paragraph that I try to rephrase as follows (see the author's webpage, or the "Online First Articles" section in the aforementioned journal webpage -- subscription required -- for the original statements):

The currently available strategies to produce as many independent extensions in the Selmer group as predicted by the $p$-adic Bloch-Kato conjecture rely on (vast) generalizations of the ideas first appeared in Ribet's gem on the converse to Herbrand (the so-called Ribet's method). Loosely, if one wants to produce elements in ${\rm Sel}(\rho)$ one picks a suitable automorphic form $f$ whose attached Galois representation is reducible, containing $\rho$ and the trivial character as (some of the) constituents, and deforms $f$ into a $p$-adic family whose Galois representation is generically irreducible; then a variant of Ribet's lemma yields extensions as the ones desired that can be shown (when one is lucky enough to be able to rule out the possible ``parasit'' extensions) to actually land in ${\rm Sel}(\rho)$. Further, for the methods to succeed, a good knowledge of the relation between the $p$-adic $L$-functions of $f$ and $\rho$ seems necessary.

What motivates my question is the following tantalizing comment of the author in the above section:

``and there are fundamental reasons that the form $f$ [as above] we work with is critical or $\theta$-critical, that it would take us too far to explain here''

(As explained in the paper, in the case of a classical elliptic cuspidal eigenform $f$, the notions of critical and $\theta$-critical are equivalent, the former meaning that there is some non-classical overconvergent modular form which is a generalized eigenvector for the eigensystem of $f$.)

Hence I would like to openly ask for some explanation on why it is so fundamental that the form $f$ is chosen to be critical or $\theta$-critical.