We are unable to have a national language, because many people disagree.
> Buddhist thought has historical played a major roles in both cultures
Buddhism was born in India, but never spread across country in any considerable amount, other countries took up on it.
The place where Buddha was born and enlightened is in modern day Bihar, you rarely find any Buddhist there.
India is very diverse, we have 22 official languages (~1000 unofficial), and for many languages writing scripts change, within 100 to 200km dialects and languages keep changing.
Food keeps changing, climate keeps changing. People's behaviour keep changing. Dressing style, music, dance,... keeps changing. Nothing stays the same.
Government have recently released a educational draft, indicating children should be tri-lingual (native language, Hindi, English) and many people straight out opposed it, indicating they don't accept Hindi, as in near future there language may go out of existence.
The main problem is we cannot communicate properly, with each other from other places.
India is in no way similar to China, except for huge population numbers.
Despite being colonized for ~800 years(600 years under Muslim rulers, 200 years under British), culture haven't changed, think how stubborn people are.
We are a mess in it's own way, but we somehow survive and flourish slowly.
A good modern day example would be, Indian election.
Indian media and left tried there best to spread anti-modi movement (~5 years), no media channel have expected modi to win majority in 2019, but it came to be quite opposite.
Even now, all media channels are doing some analysis, how did this happen.
There is an old saying ( loosely translated),
If you are having a discussion with 5 chinese and 5 Indians about a problem. All Chinese come up with one solution, Indians come up with atleast 6 different ideas.
Thank you.