In Baseball Prospectus, Ryan Wilkins tries to argue that the strike out is not as bad in reality as it is in perception. But he seems to be conflating two separate arguments. The strike out vs. putting the ball in play, vs. the strike out vs. other outs.
It’s certainly true that the strike out is not the worse thing that can happen to a batter. Whenever the bases are loaded it is certainly better to have player strike out than hit into a double play. But I haven’t seen anyone argue otherwise.
The reason why people argue it is better to put the ball in play is not because it can result in a better out. It's seems a bit obvious, but the reason you want to put the ball in play is because you have a chance to get a hit! Putting the ball in play gives you a 25% chance of getting on base, while striking out gives you something pretty close to a zero chance of getting on base.
He also runs a regression that shows strikeouts actually have little correlation with runs scored. But the strike out does have a positive correlation with such hitting stats as isolated power and slugging percentage. But this is actually pretty intuitive and doesn’t tell us much about the value of striking out vs. other types of out.
Sluggers and free swingers will usually have high totals in slugging %, ISO, and strikeout. While contact hitters would have lower percentages in all three. The correlations between these statistics just confirm what should be common sense. It does not tell us what value, negative or positive, strikeouts have in relation to other types of outs.
It would certainly be better for the slugger to strike out less and put the ball in play more, but only if it would not take away from his power numbers. This is usually a trade off most sluggers have to make.
If you don’t have much power it doesn’t make sense to swing for the fences. You can increase your chances of getting on base by just trying to put the ball in play. The regression analysis quantifies the tradeoff between contact and power.
Anyway, later in the column Wilkins undercuts his own argument by showing how stikeouts have a very high correlation with a pitchers ERA. Isn’t hitting/pitching a zero sum game? Why yes it is. So anything good for the pitcher is bad for the hitter.
The bottom line is that the strike out is rarely a good thing for a hitter. But given the fact that the strike out will always be somewhat correlated with positive hitting statistics, it will be very hard to quantify exactly how harmful it is.