There is an entirely false equivalence:
Pakistan: Islamic country, history of "discrimination and religious persecution"(BBC) against Hindus of all castes.
India: Majority Hindu country, history of discrimination against Muslims. Casteist discrimination also prevalent.
So Pakistani Hindus can expect to be better treated in Hindu majority India than in Pakistan. They would not expect to be coerced to convert to Islam. They can openly take part in Hindu ceremonies, rituals and festivals.
Indian Hindu Dalits and other people in scheduled castes would not expect to be treated better Pakistan. They would still be poor, not have access to education. In addition, they would also be subject to religious discrimination, or pressure to become Muslim.
So there is no "pull" to move.
Moreover there are considerable barriers: Pakistan does not grant visas to Indians, except for business, to visit family, or as pilgrims. Dalits (in general) do not have these options. In particular the "pilgrimage" visa requires you to prove that you can support yourself financially. If impoverished people in scheduled castes attempt to cross the border they would be rejected. If caught they would be returned to India. Pakistan does not give general refugee status to people in scheduled castes, unless there is specific evidence of a fear for safety.
So there is a big "push" reason to not to go to Pakistan.
Finally it is not so easy to move. Moving costs money and with 33% of scheduled caste members living in poverty, moving is difficult. You home is where your family is, where you can get support from members of your community, even if you face discrimination from other members of your community. You have some land, some money, some shelter. If you move, you have to start from nothing.
There are considerable pull reasons for staying put.
Now for any individual will need to consider the pull and the pushes. For the vast majority of people in scheduled castes the calculations goes like this
|Reason to go
||Reason not to go
||Can't practice my religion
||Can't get visa
||Can't afford journey
||Don't have friends and family
||Dont live at home
When you compare like this, the reason why people in scheduled castes are not trying to go to Pakistan is pretty obvious.
Of course there are some members of scheduled castes who are now successful entrepreneurs. Most could easily afford to obtain the paperwork to enter and live in Pakistan, but far prefer to have a penthouse apartment in Mumbai or Dubai or London. I leave it to your speculation why this might be.