I have only been in this craft for more than forty years and recall reeling in horror the first time seeing someone 'stone' a mill table.
I have watched a series of videos by a very experienced and skilled man I have great respect for (never meet in person) who practices this 'stoning' religiously.
I am vehemently opposed to this as a routine practice - No, I will not do it! It is for repair only.
I commented on a Haas video that is excellent except for the practice of stoning - should not need to be routine and should be a video in itself.
I completely dismiss the idea this is routine - sometimes you have no choice but most times a spritz of your favorite fluid or even the machines coolant. Steel wool or fine scotch brite is all that is needed, rinse again with your fluid and wipe dry with clean rag.
If ever I do stone tools such a parallels and the like it is to remove the nicks and burrs left by the dull and ignorant. And that is with a very fine and soft Arkansas stone, done carefully. Be mindful of your tools and surfaces and you will rarely if ever have to do it.
A few times I have used a large stone as described above to restore tooling and machine tables that had been neglected. A few times just the spot where a tool loading tragedy raised a divot.
Never ever lay steel tools on the machine surface. I don't mind squeaky chalk but that clink of a wrench gently set on a table I hear from across the shop over the din. That is my burden. I always have a rag, cardboard, or even a scrap of aluminum sheet to lay tools on.
All this being said - if you insist and are compelled to do this, read post #13. This is a skill, not just rubbing a rock.
You do what you feel is best for yourself and your tools.
Me, I am ever so kind to precision surfaces and they have served me very well.