OK, let me try to explain better.

In your example, the only thing that prevents me to invest in the source A (with the ridiculously high EROEI) is how much other resources than energy I currently have. For example, say source A requires diamonds, which are expensive, and I can only afford a handful. But source A is much better investment than the source B, and I absolutely want to invest into A first (at the very least, I can sell the energy with much higher profit margin).

In my example, the only thing that prevents me to invest into higher-yielding asset (and we agree it's a good idea) is some additional limitation of reality (availability of resources), for example the size of the market.

So in both examples, there has to be an additional resource constraint, which prevents putting all investment into the higher-yielding enterprise. In the first example this limiting resource is money, in the 2nd example it cannot be money, but it can be something else.

So if ROI is a good way to compare investment opportunities, EROEI is a good way to compare energy sources.

> It may be more difficult to fake, but it does not answer the question what use the measure has.

An well-known example where ROI was faked is subsidies for ethanol as energy source. EROEI is less than 1, but because of the subsidies, ROI became larger than 1.

The EROEI would be an ultimate measure of where to put your effort (energy) if you were alone in the world and there were no other people. Then you wouldn't need money and could price everything in energy required to obtain it. Or equivalently, the world where people would collectively want to minimize the amount of effort they want to spend. Which is not quite the real world with money (the wealthy people for example can afford less effort than others), but it's useful as an approximation of it (and if you assume free market, then they are very close).