Yes, the 3 foul rule falls under "standard One Pocket" for sure.
I put that in there because several posters commented on the question of golly gee, how do you keep score if you are spotting up balls? The answer is simple, just like standard One Pocket when it comes down to the last ball. It's not in the "rules" -- it's in the addendum that -- based on the comments in this thread -- some of which is only basically necessary for nits, anglers, old farts and maybe TD's lol.
You are right in pointing out that the only version with foul limits that I included above is the "Sudden Death" version. That is because I did not hear a lot of support in this thread for other limits, such as the one I first proposed of no more than two balls on the table for any player, or the next foul/scratch would be loss of game. And the Sudden Death version is certainly a LOT EASIER to define and explain than a limit of 2 or more balls per player. So I began to think those other options were unnecessary. Of course as you are well aware, players can agree to play however they want -- unless they are in a tournament that specifies obviously.
That's also why I put a TD's option if they get a stubborn player taking advantage if there is no actual penalty for multiple re-breaks. Everybody else can just ignore that because it would, as you essentially are saying, be unnecessary.
That said, I am still listening, so please keep the comments coming -- everybody -- even if all you want to say echoes what somebody else already said. In fact that tells me that more than one person is concerned about that particular point. So keep the comments coming.