The various borders [of India] are manned on the concept of ‘one border one force’. The sanctity of international demarcated borders is the responsibility of Central Armed Police Forces. The Line of Control (LoC), Actual Ground Position Line and Line of actual control (LAC)remain under the operational control of the Indian Army. During war, all border guarding organisations come under the operational control of the Army. Being the first tier of defence, their integration, training and operational procedures must provide seamless transition to the war fighting effort.
That is from the recent Indian joint doctrine paper.
One, notice the terms used to describe the border. Does America have a "Actual Ground Position Line" with Canada or a "Line of Actual Control" with Mexico?
Those are some seriously contested borders.
Two, notice that unlike our customs and ICE people on our borders who try to keep illegal migrants and criminals out, the Indian border security forces are considered the first line of defense in case of invasion and are integrated into warfighting plans.
That is a dangerous neighborhood.
Compared to India's land concerns, consider how little force America needs to defend our borders (compared to China in this post).
Russia has the same problem but it is even worse given the poor force-to-border ratio.
India might want an ally rather than a friend.