"Why it's so difficult for gambling websites to get backlinks from non-gambling domains?"
It's not difficult.
Well yes, it is if anyone is looking for links for 'free' (ie to content that is worthy of a link without financial recompense or other incentives). There are many (obvious and perhaps...
Yeah, it's not just volume, but it'll need to be 'volume that's worthwhile'.
You'll most likely need to demonstrate the volume and show how that volume is being generated (ie the geos and search terms/traffic sources that are driving it).
And evidence suggests that when you've pulled that...
Yes, you can.
But..........first of all...... make sure that the home page is not ranking for any terms that are contained in the content you're going to remove....or that the content you're removing isn't supporting the home page to rank in some way. If it is, you have some thinking to do.
If...