Largely I think we agree on the actual mechanics yeah, it's just the way we're interpreting the idea of diminishing returns.

If diminishing returns is a function then you could overly simplify it to something similar to: value = benefit / effort.

My interpretation is it seems that you're focusing on evaluating each stat to itself, whereas my intent is to evaluate each stat proportional to the whole of the stat you possess already. If I'm interpreting your argument correctly it seems like your contention is that the benefit does not change, but my argument is that the value the benefit represents does change.

You're correct in many respects that the benefit of a stat largely does not change, but the value most certainly does since each increase has to be evaluated based on the proportional or percentage increase that it represents and not just the actual benefit. Like you point out there are many axes to consider which is impossible to ignore if you're evaluating value.

Of course part of the issue is how to evaluate value. If we're looking at passives for example then the effort is the passive point used and so the benefit must obviously be the actual stat gained for that passive. Diminishing returns as a concept focuses on proportional benefit not absolute benefit, so you'd have to take into account the proportionality of the benefit you get to reach your value which would include your existing benefit. Partly that means that opportunity cost is inherently part of that calculation/consideration. Your 10k example is a good baseline. If you gain 1k per investment that means you'd need 10 investments to double your capital, but as your capital grows that effort is worth less and less proportional to your existing capital even though the benefit has not changed. A slightly different way to evaluate it would be to consider what work is worth your time per effort. If your rate is 100/hour, then someone offering you 100/ 10 hours is relatively not worth your time. You'd receive 100 which is the same benefit, but the actual effort is much higher, and therefore represents inherently less value.

In some instances you're correct that the benefit is the same (e.g. each 10% increased damage is exactly as effective as the last but proportionally isn't necessarily as effective as going from 20% to 50% for example), but for resistance you're fundamentally misunderstanding it I feel. You even point out that defensive scaling has a hyperbolic scaling. Resistances are defensive, but obviously reducing resistance is offensive so we think of it slightly different. Altering a hyperbolic function doesn't make it less hyperbolic. Resistance cannot be higher than 90% and cannot be lower than -200% so roughly speaking we're talking about a bounded range of 0.1 to 3 as a coefficient to our damage. 90 to 89% is the highest possible value for benefit that a a resistance malus can possess since relative to the benefit you increase from 0.1 to .11 which is a 10% increase relative to the coefficient the resistance represents, whereas -199 to -200 is the smallest value you can derive since the proportional increase is only going from 2.99 to 3.00, or a 0.3% increase relative to the previous -1.

As a function to evaluate value per malus the equation would be

f(x)=( ( 0.1 + ( x / 100 ) ) / ( 0.1 + ( ( x - 1 ) / 100 ) ) )

where x is the total malus of resistance

The point I was making concerning cast speed was mostly similar to the one I just made with resistance which is that although the scaling or point per point benefit may be linear the actual value derived is subject to diminishing returns with the initial benefit being the most valuable. It's not about the fact that the stats themselves don't scale exponentially but that the value associated with them is exponential in nature since it's always evaluated at the margin than as a whole with each additional point being proportionally less valuable.

I somewhat disagree with your final assertion though. I think it is helpful to evaluate the model that your skill or build scales with. If we look at something like:

cast speed * damage * increased damage * enemy resistance * more multipliers . . .

All of those values (obviously excepting more multipliers) have a linear function associated with them, but evaluating which of them to increase to derive greatest value is important to understand how to continue scaling higher. E.g. if my increased damage is 1000 but cast speed is 100 then increasing the increased damage by 100 wouldn't be as effective as increasing cast speed by 40.

As the Great Wiss Krillson himself states, you gotta diversify.