How deep can you sand into pine flooring?
I don’t buy the “blotchy or discoloration” claim. Sanding doesn’t bring the blotchy problem out. If it wasn’t blotchy before, it won’t all of a sudden develop a blotchy appearance. 

Blotchy areas are caused by pockets of sap, chemicals, stacking problems, etc. Here is an article that explains:

https://hardwoodfloorsmag.com/2018/07/31/common-stains-discolorations/

Yes, refinishing wood floors are sanded down through the finish. Often we’ll refinish school gym floors. The finish (and painted lines) are sanded until they’re gone. Then we use a light “pre-stain” to help eliminate any possibility of blotchy finish. 

The real sanding depth issue is sanding down so many times that the nail head begins to show. Usually we can sand a gym floor 3-4 times before we need to replace it. 

BTW, I doubt that it’s pine. Floors are made from hardwoods.