Defying power scaling:
Introducing a Non-Action Big Bad is a great way to prevent power scaling from getting out of hand, especially if the previous Big Bad was a case of Rank Scales with Asskicking. This kind of villain brings to the table challenges that can rarely be overcome with brute force alone. Therefore demanding the heroes to employ the tools they already have or develop skill sets that don't depend on acquiring more power. There's something to be said about beating the bad guy at their own game.
Non-action villains often rely on money or political influence (and sometimes sex appeal) to get things done and thwart the heroes' attempts at reaching them. After all, in a straight fight, a Badass hero is pretty much ensured to get rid of the Big Bad with little trouble. A wealthy villain can be hard to reach because of all of the cutting-edge technology securing their lair. If they know the hero's identity, then the villain can threaten their economic stability. On the other hand, a political-savvy villain knows how to twist the facts so as to make themselves the victim and undermine the hero's credibility. It's very likely they've amassed tons of followers and have friends in high places, thus making them a Villain with Good Publicity. A sexy villain can set a very devastating Honey Trap to learn the hero's weaknesses. They can also stir a conflict between the hero's love/desire and duty/morals.
As such, it's not always a case of fighting smarter instead of harder, sometimes things are just more personal. Nor does it mean sheer power won't be needed sometimes.
If done right, this trope can be very refreshing. If anything, it can be used more than once because it's simply more versatile than a combat-oriented Big Bad.
Difference with Weak Boss, Strong Underlings:
As noted on the main page, chances are the non-action evil mastermind hires/builds Mooks and even a second-in-command who are way more adept at fighting. So these two tropes usually overlap.
The difference, however, is that the minions can be non-action guys too. It all depends on the story that is being told — in an office setting, for example, trying to punch the big bad will only get the hero arrested. Same if the story is about a familial dispute or some sort of talent contest.
So, a non-action big bad isn't actually required to be stronger than their underlings, they just have to not be badasses. Furthermore, Weak Boss, Strong Underlings can also apply to heroic or neutral characters.
