“India is Indira and Indira is India” is just a sign of the tendency towards personality cults that the polity suffer from. In fact, it was not Indira who coined the slogan, but rather a particularly oily sycophant, D. K. Barooah [1].

In fact, in some sense, there is an attempt to try to deify/lionize the PM as a royal. I don't think that it is a symptom of the failure of parliamentary democracy, rather it is a tendency among people.

[1] https://en.wikipedia.org/wiki/D._K._Barooah