I never got to play around with sodium additives directly but I'd offer up the following thoughts...
Sodium sulphonates are as old as the hills. Back in the 20's & 30's it was common practice to react raw base oil with sulphuric acid/SO2/oleum. Some of the more reactive aromatics in the base oil would form sulphonic acids which could then be reacted with caustic soda (sodium hydroxide) to give so-called 'natural' sodium sulphonate. I may be wrong but I can't think why anyone would put sodium sulphonate in a modern US engine oil. It's TBN is extremely low and although I'm no chemist, I'd have thought it would be quite difficult to over-base sodium sulphonate to give it appreciable TBN. From a TBN point if view, it would make far more sense to get your TBN from calcium or magnesium (plus the tiny contributions you get from diphenyl amine AO and ashless dispersant).
Putting sodium alkyl thio-carbamates in modern oils as friction modifiers might make more sense assuming they do indeed function as friction modifiers. Molybdenum dithio-carbamates are proven, effective friction modifiers. They are however 'locked in' by various patents and are eye-wateringly expendive to buy. If the corresponding sodium analogue showed some friction reduction performance, even if it was worse than that of Moly, it might give you more IP 'freedom to practice' and be way cheaper. These additives can't be particularly complicated to make and sodium salts are generally cheaper than moly salts. The same goes for potassium and lithium salts.
Having said that, I might have concerns about putting sodium salts in oil. Sodium is far more polar and reactive than calcium, magnesium and molybdenum. I might worry about how the oil interacts with water (which inevitably you get in your sump) and the potential for forming emulsions. I might also be concerned about how this stuff might interact with the other additives in the oil. Presumably Valvoline had checked all of this out as part of the oil approval process but if I've learnt one thing over the years, it's that the approval tests do not guarantee the absence of problems in the field, so I personally might avoid such oils.