ah, ok. well, I guess you *could* use it that way (but I’d ask: “what inverter? how is it laid out? what is its physical aspect ratio? how big are the power and ground rails? How *big* is the inverter?) On a given process node, there are an infinite number of possible inverter designs. Even putting aside layout variations, there are sizes. I would guess in this scheme you propose, we would be talking about what I would call an INX1, driving an INX4 (or driving 2 INX2s, or driving 4 INX1s), where an INX1 is the minimum possible drive strength - in CMOS this would be W/L=1 for the NFET, and in FINFETs I guess that would be a single fin.
I’ve never heard of anyone using this as a metric - certainly we never did - precisely because there are a lot of questions there. You have to make a lot of assumptions about what this inverter is, and it’s not very useful for extrapolating to other more complicated gates (because, for example, NFETs and PFETs scale quite differently, and a given process may have backside power, or SOI, or some other feature that makes it so that comparing inverters on 2 processes tells you very little about comparing two multiplexers or two NAND gates.
What FO4 has always referred to, in my experience, is the rule of thumb that designers use when deciding how to size gates. In other words, if you need to drive 4 INX4’s, you probably want approximately 1 INX4 driving it (or 2 INX2s, or whatever).
I often say “I’m not sure” or “I’d have to think about it” re: questions here, but I can say the following additional thing with absolute authority, because I was the timing czar for a long time at AMD, wrote a lot of our timing tools, and worked with synopsys to show them several mistakes in the way their timing tools worked, which they then fixed. Even on a single chip, fabricated on a single node, if you have an INX1 driving an INX4, it will almost never have the same gate delay as an INX4 driving an INX16. In fact, that INX1 driving an INX4 will not have the same gate delay as another INX1 driving a different INX4. There are just too many variations in lots of parameters. So to make FO4 a metric instead of a rule of thumb, you’d have to specify all sorts of things: input slew rate, physical gate size, which drive strength are we using, assume zero wire capacitance and resistance (or specify what R and C are), temperature, etc. Small changes in these parameters can have huge effects.