It an interesting subject. First I guess we are talking about the elite/landed given the masses didn't really have much say/decision on the political scenarios (till recently).
My take on it is the main factors are:
a) The turmoil created in the subcontinent caused by so many different competing political forces (that allowed the voids needed for foreign forces to break into and exploit for their political and economic gain etc)...so people inherently grabbed the opportunity (in early 20th century till its final fruition after WW2) to have as large envelope afforded to them politically as possible that fills in behind the larger cultural space/connections created over much longer time period.
b) The early rule of (Nehru) congress did accomplish some very core things at mass level (federally) that are often sidelined today. These are things like land reform, access to political vote (sustainably), good development oriented state leaders and promulgating strong and needed state institutions... i.e things could have turned out quite different in India political stability if 1st leader was a despot and did something like Indira Gandhi did (later) with emergency powers etc....from the get go.
Of course over time because of larger aegis of socialism/leftism, congress inevitably drifted from its realisation of the potential the country offered....but there is no escaping that the pragmatic optimism of the 50s till mid 60s etc were instrumental in ensuring a deep set nationalist thread in all parts of the country to the level needed to propagate long term....esp combined with the percetion of point a).
c) There were single unified country dynamics taking root post-Mughal prime (Maratha Empire is best example) that probably would have accomplished something quite large (as far as concept of united indigenous realm) had the British not arrived when they did and upset that....and substituted their own version of it. So the overall concept was not that foreign to India (probably given the larger cultural realm hewn out even with the different polities in existence)...but rather whoever plays the highest stakes game the best ultimately won the hand (politically).
Things like Marathas going very easy on British after their victory in the first anglo-maratha war for example....they definitely regretted that in the end....but its too late at that point....often how centuries of history turn out hinge on knife-edge single things like that.
@anant_s @Kashmiri Pandit @DarkPrince @Gibbs @Hell hound