In the book The Quantum theory of fields Vol. 2 at page 193 Weinberg says
$$ \mathscr{L}=-\frac{1}{2} \partial_{\mu} \phi_{n} \partial^{\mu} \phi_{n}-\frac{\mathscr{M}^{2}}{2} \phi_{n} \phi_{n}-\frac{\lambda}{4}\left(\phi_{n} \phi_{n}\right)^{2} $$ where $n$ is understood to be summed over the values $1,2,3,4$, with $\vec{\phi}$ an isovector pseudoscalar field and $\phi_{4}$ an isoscalar scalar field.
The immediate problem faced by any sort of effective Lagrangian is that in order to use it to calculate scattering amplitudes, we must either include all Feynman diagrams of all orders of perturbation theory, or else find some rationale for dropping higher-order diagrams. We can find no such rationale with Lagrangians like (19.5.1), in which the broken symmetry is realized through linear transformations on the various fields.
Why is that if the broken symmetry is realized linearly we can not find rationale?
