But that doesn't make much sense in comparison to evaluating system performance. A Pentium III could have a billion FP32 operations given almost 16 years, but you wouldn't say its 1 GFLOPS. Assuming the "S" is seconds, it becomes a useful metric and we can say it has 2 FLOPS.

Then it should be "FLOPs" to indicate that the S is not separate word in the acronym, just the plural form.

It’s not an acronym, it’s an abbreviation. Unfortunately, the rules for abbreviations are effectively arbitrary (or specific to some etymology that’s not available from context). The “s” could be op(s) or seconds, but back in 90s trade publications it was seconds.