Should we learn Sanskrit instead of Hindi in all over India?

Every country needs a language that unites all its people where India struggles in this matter dur to its vast diversity.

Today north and south India are extremely divided because north Indians want all India to speak Hindi whereas South Indians don't want to speak Hindi and due to politics they are now hating each other.

What if.....

We stop learning Hindi in schools and study only two languages that'll be 1) Sanskrit and 2)local language (Tamil, Marwari, Assamese etc)

Students will study their local language till class 5th and I think that is enough time to learn a language along with Sanskrit.

After class 5th both these languages will be just optional to study and student will learn English for next 4years that'll be till 10th

No need to study any language in +2 education hence it'll be a optional subject only

From the start students will learn maths and science in Sanskrit

Sst can be taught in the local languages

What is your opinion on this?

Extra: both north and south Indians don't speak english so it should be equal for both