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The charts come from here, it's an excellent tool that I've used for years The notes give some guidance on applicability. The charts are best used for comparing performance within one specification type e.g. comparing the different MB specs but are not necessarily 100% accurate across different specification types e.g comparing API specs with MB specs.

Relative Performance Comparison Tool for Passenger Car Specifications - Engine Oil Additives - The Lubrizol Corporation

 

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The second is that they show a list of properties, but it is not clear if this is an exhaustive list that contains all of the relevant properties of engine oil?

No, not exhaustive.
Looking at the parameters in post #59, oxidative thickening is countered by use of anti-oxidants. No mention of the contribution to oxidation caused by aeration/foaming. The ensuing parameters are all negatively impacted by aeration/foaming. API-CK-4 addresses aeration/foaming, API CF does not.

MB will not grant approval without being furnished with the 'ingredients' of the product. Not every lubricant manufacturer is prepared to do this. If however, you have no technology worth guarding then meeting an OEM spec is as simple as including the approved additive package. Note, use of additives as remedial not preventative eg, oxidation.

Additive packages deplete in service. That there was enough straight from the carton to meet the OEM's spec is no guarantee that there is enough during service. A base oil and supporting chemistry that is less dependent on additives as remedials because it is preventative by nature depletes its additive package more slowly. An oil manufacturer that deviates from the prescribed additive package preferring its own proprietary solutions will not get OEM approval without divulging its knowledge. Hence API CK-4 oils without MB approval.