US does not even have a no-first use policy. And they simply do not want the countries vulnerable perpetualy to their threats heave a sigh of relief on this count.
They have actually have enhanced the threat level to non-nuclear nations to almost alert level, and this was done unilaterally without any consultation with other nations nor even with any democratic debate within US itself.
With such track record, to expect a reciprocal gesture from India would surely not include making India's security doctrine answerable to them is not in consonance with the nature of the negotiation.
A non-aligned India simply does not seek such intervention.
Further, the nature and the qualitative charachter of the doctrine would change with the context and configuration of threats. Expecting India to bind itself to any formal definition is untenable from Indian policy framework.