Perhaps renewable fuels is more accurate but is the wind considered a fuel and the thermal mass of a passive solar house also a fuel? Is the water behind a hydropower dam a fuel? Wood is a renewable fuel only if the land is properly managed. Ethanol could be a renewable fuel if the fossil fuel inputs were eliminated. Getting hung up on semantics with writers who are scientific illiterates doesn't help the cause of eliminating fossil carbon fuels.

I would go along with you in a profound scepticism of most EROEI calculations, but on occasion where it is kept fairly simple then it can have some approximate use, for instance in showing the absurdity of ethanol from corn.

Mostly of course it is used as a polemic to diss whatever energy source the writer dislikes, rather than with any more profound analytic intent.

The term "renewable" is perhaps unfortunate. Perhaps a better term, though somewhat unwieldy, would be "local, current, solar energy, be that photovoltaic or wind or bio or whatever".

Definition of renew:

To make new, or as new, again; to restore to the same condition as when new, young, or fresh.

Oxford English Dictionary

Hence the term renewable energy because a renewable energy source is constantly renewed/replenished from another (usually the sun). Renewable is completely different to reusable. There is nothing incorrect about the termrenewable energy as this refers to the replenishment of the energy source, not to the constant recycling or reusing of the same energy. Reusable energy would certainly be a stupid term, which is probably why no one uses it.

The sun is ultimately a finite source of energy, but this is not really relevant on a human timescale. The output of the sun is not under human control and the sun is not 'depleted' by human activity as other energy sources (such as fossil fuels) are.

As for EROEI, that fact that it can't be measured exactly does not make it meaningless. The declining EROEI of oil for exmaple, can be shown by reference to increasing rig counts and footage drilled. As a smaller subsystem within a larger one (your 'oikos'), the human economy is subject to the same laws governing energy capture and use as any other smaller system (e.g. ecosystems and individual organisms). Of course EROEI calculations can be biased and manipulated just like any other statistics but this does not make the concept of EROEI meaningless.