The main reason this fits as well as it does with the era it's set in is that Paul Cornell really doesn't like the Seventh Doctor that much.
Oh, don't get me wrong; he's a Doctor Who fan and always will be. But he's a fan because he admires certain qualities in the Doctor--his sense of whimsy and magic, his essentially romatic nature, his irrepressible joy at the human spirit. The "sweet" side of the Doctor. He's deeply conflicted when he has to write the Seventh Doctor, that sinister manipulator and player of games with the darkest of monsters. It's not that he doesn't understand that they're two sides of the same person, and that the whimsical Romantic sometimes gives away to the terrifying monster-to-monsters that the Doctor can be...but he's not comfortable with it. Virtually all of his Seventh Doctor stories exist within that tension, and explore it like a scab that just won't heal.
And 'The Shadow of the Scourge' is no exception. The front half is mainly about the Doctor coming up with what Cornell thinks of as one of his "typical" plans...although it's really only typical for a Cornell Seventh Doctor story. When other authors describe the Seventh Doctor as doing something that will eventually come to be known as "timey-wimey", it's usually presented in the form of a benevolent predestination paradox; the Doctor discovers that events have already been arranged in a particular way, and ruefully assents to being history's puppet just one more time. Whereas Cornell always describes it as weeks of tedious stage-managing in order to make sure the latest caper goes off without a hitch.
It doesn't work, of course, because it never works. The halfway point of the audio marks the end of the first act as all of the Doctor's manipulations are undone, forcing him to improvise desperately and to rue and regret his manipulative ways. The former happens in most of the Seventh Doctor's stories--after all, it'd be a pretty poor piece of drama if the Doctor solved everything in the first fifteen minutes. But the second part, the Doctor confronting his personal flaws, is unique to Cornell. In that respect, 'Shadow of the Scourge' is a close cousin to 'Timewyrm: Revelation', to 'Love and War', to 'No Future' and to 'Human Nature'. It's an analysis of the fundamental contradiction within the Seventh Doctor, the dynamic between his callous and cruel manipulations of his friends and of strangers and the ultimate rightness of his actions when all is said and done.
So the back half is mostly about the Doctor beating himself up over being such a jerk to his friends, and because he wants to explore that theme, Cornell uses the Scourge as a villain precisely because they're using his own conscience as a weakness. The Scourge point out everything Cornell's thinking--that his overplanning and arrogance were used as a weakness against him, that he was used as the Scourge's weapon against humanity precisely because of his conceited belief that he could stage-manage one of the oldest and most powerful races in the universe to death with just a few parlor tricks. It overreaches, perhaps, in suggesting that everyone can defeat their own private Scourge simply by remembering the small and simple pleasures in life...not only does it weave unsteadily across the line between sentiment and schmaltz in places, it's also unfair to people to suggest that they always have the power to defeat their own private demons if they'd only think happy thoughts.
But ultimately, the point of the story is that optimism and hope are stronger than despair, that friendship and unconditional love can defeat the worst things in the depths of our souls if we'd only reach out and ask for it, and that people have an enormous capacity to forgive, if we only extend our sincere repentance. Oh, and that cute babies and long parties with tea are pretty damn awesome. Those are messages worth having around, even if they do come with a bit of schmaltz on them. (It brushes off.)