I would have thought this was so obvious it didn't need explaining, but apparently I didn't do a good enough job of making my case today on the Sirius XM show because Paul Sporer came away still thinking FPS% is a thing. So let me try again here.
For a metric to be useful it must measure some predictive skill. Strikeout rate is useful because it measures a pitcher's ability to get outs without contact. Contact entails risk, strikeouts do not. If past strikeouts are predictive of future strikeouts (they are), then looking at strikeouts is meaningful. Even if two pitchers had the same ERA in the same number of IP with the same WHIP and same number of walks in Year N, if Player A had 200 Ks and Player B had 150, we would expect Player A to be better in Year N+1, barring some demonstrated skill by Player B (extreme ground ball rate, soft contact, etc.) to offset it. All things being equal, the strikeouts would mean something.
We could say the same for swinging strike rate as it measures the ability to miss bats, which is predictive of strikeouts, which are predictive of run prevention. There are many metrics for which we could go through this exercise, and as long as they measure a skill that's predictive going forward, they are meaningful.
But first-pitch-strike rate fails this test. If Pitcher A and Pitcher B have the same numbers (Ks, walks, ERA, WHIP, etc.), but A has a better first-pitch strike rate, what does that mean about him? That he has better control? No, if both pitchers have the same number of walks and Ks, the same number of strikes and balls, then A does not have better control even if his numbers show better control on the initial offering. Necessarily, B had better control on subsequent offerings, as they wound up in the same place.
Control and command are no doubt important and predictive skills, but for FPS% to be meaningful, it would have to be an indicator of control and command above and beyond the pitcher's overall body of work. Put differently, if a pitcher has x number of strikeouts and y number of walks, or p number of strikes and q number of balls at the end of the year or month or week, the order in which those strikes and balls came don't matter. To establish that the order mattered, you'd have to show that throwing strikes on pitch 1 is a more predictive skill with respect to control than throwing strikes on subsequent pitches. Otherwise, control is control, and while it's obviously an important skill generally, there's nothing especially important about the order in which the strikes and balls come.
The fact that throwing a first pitch strike correlates with better outcomes than getting behind in the count is not a refutation of the above. Just as scoring the first TD in an NFL game correlates more to winning than having the first TD scored against you, teams that have happened to score early in games do not possess a special "early-scoring" aptitude. If a team scores 350 points on the year, we don't look to see whether they were good at getting out to early leads and use the "when a team is ahead by seven, they win 60 percent of the time" stat (or whatever the exact number is.) We realize it's meaningless because we know the overall output and record of the team. The sequence of the touchdowns is unimportant, even if scoring TDs generally is obviously important. The early-TD scoring stat would have to reveal a skill about the team's ability to score above and beyond its total output. Yards per play is such a stat, for example, but first-TD scoring is not.
Similarly, to establish FPS% as something meaningful, you'd have to show that there was a specific skill to doing it on that pitch as opposed to generally, i.e., that the first pitch was especially indicative of a pitcher's control in a way beyond the overall control metrics (balls, strikes, Ks, walks, etc.) generally.
Obviously, if we knew nothing else about pitcher A except that he threw more first pitch strikes than pitcher B, we'd prefer A because strikes are good. Just as if we knew nothing at all about two NFL teams except that one usually had a lead after the first quarter and the other usually was behind, we'd expect the leading team to be better. But with a player's or team's entire stat profile over which to look, that's never the case.