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A good term for 10^20 FLOP would be useful. This would make modern models around 100k to 10 million of this unit, which is a tangible number. Some people, e.g. at DeepMind tried to make "petaflop-days" (8.64e19) a thing but it didn't catch on.
The 100k to 10M range is populated by abstract quantities—I think that for a measure to be useful here, it has to be imaginable.
Avogadro's number has the benefit of historical precedent for describing quantities, and the coincidental property of allowing us to represent present-day training runs with numbers we see in the real world (outside of screens or print) when used as a denominator. It too might cease to be useful once exponents become necessary to describe training runs in terms of mol FLOPs.