I'm in agreement in principle...the idea that you either adopt the arc flash analysis method in 70E or you do your kwn, but not to mix them. The PPE part though is the same for either system. So I could call in "local PPE" 1-4 and be done. This rule made more sense when the idea is that it was a combination of hazard and risk but no more.

I can understand this a bit but then I would be guessing the NFPA’s thought process. Only reason I can see were this would make sense is to simplify the labels and cause less confusion.
Either you state the PPE level, the worker does not need to know specific incident energy he just needs to know the level of PPE’s to wear.
Or you print the incident energy and you school your workers so they know how to select PPE with a given incident energy.

I might not give the common worker enough credits here but you read a lot off ‘painful’ errors when you read about arc flash incidents but here are a few things that come to my mind that could happen when you print both incident energy and PPE category:
The worker sees PPE level 4 and energy 35 cal/cm2 but on another label he sees PPE level 4 and incident energy 28. Result is confusion unless workers are schooled in PPE categories and incident energy.
The worker sees incident energy 9 and PPE cat 3 on the label and decides to wear cat 2 PPE’s because it is not much higher (this can technically also happen when you just print incident energy).
There are also cases when I calculate 40 cal/cm2 in 2 different situations, one results in cat 4 the other results in NO PPE EXISTS. This also leads to confusion but do note that the 40cal/cm2 does need to be rounded up or something when you just print incident energy.

The thought process that says "printing either one is "good" and provides "enough" information,
but having both is "bad", completely eludes me.

If having both leads to "confusion", doesn't that really imply that one (or both) are wrong to some degree?

So, if you are going to print only one, which do you choose?

the problem is that the category is meant to represent assessment of both hazard and risk, developed through strict parameter limitations.

The category listed on the label does not represent the assessment of both hazard and risk. If you use the tables, your only real option for the labels is to show the, "highest Hazard/Risk Category (HRC) for the equipment". So, the category shown on the table is for the highest risk and any reduction in PPE based on a risk assessment must still be determined.

The real benefit of the category system is that it provides a simple way to refer to the PPE requirements listed in table 130.7(C)(16). If the PPE listed under HRC 2 provides good protection for equipment with IE between 4 and 8 when using the tables, why isn't it good for equipment with IE between 4 and 8 that was calculated?

"Serious misconceptions have crept into this field of research through adoption of rule-of-thumb terminology which has lost its identity as such and become accepted as fact. A glaring example of this process is the 'critical thermal load.' This quantity is defined as the total energy delivered in any given exposure required to produce some given endpoint such as a blister. Mathematically it is the product of the flux and exposure time for a shaped pulse. Implicit in this treatment is the assumption that thermal injury is a function of dosage as in ionizing radiation, so that the process obeys the 'law of reciprocity,' i.e., that equal injury is produced by equal doses. On the contrary, a very large amount of energy delivered over a greatly extended time produces no injury at all while the same 'dose' delivered instantaneously may totally destroy the skin. Conversely, measurements of doses which produce the same damage over even a narrow range of intensities of radiation show that the 'law of reciprocity' fails, for the doses are not equal."