It's a very funny show with crisp writing and nice comedic delivery by good actors, and there are plenty of characters to recognize from any large institution including public ones, but on the whole it's basically superficial Thatcherite propaganda made by people who aren't trying to convey real understanding of the systems they're criticizing or consider the context or alternatives. A real Chesterton's fence situation. You can see where a few decades of the same soundbyte-driven antisocial mentality has landed the UK; Brexit is the coup de grâce.
Of course they're not considering the context or alternatives. They're holding up a mirror; nothing more. This is a comedy show, not a political science thesis.
In fact, they went to great lengths to avoid making the show content partisan. It was ridiculing the system, not any parties in particular.
I fail to see in what way this is a Chesterton's fence situation... They're not recommending any course of action at all; merely showing what a mess politics can be.
The ridicule is (well written) cheap laughs from a mostly Thatcherite direction. The same ostensible critique of "the system" (i.e. the British civil service) was a cornerstone of Thatcher's whole career and political movement. They didn't need to specify parties, and it's no surprise why it was Thatcher's favorite show.
It's a similar mindset as Reagan's "The nine most terrifying words in the English language are 'I'm from the government and I’m here to help.'" Sure, folks should have some healthy skepticism of unsolicited offers from anyone including the government, but adopted literally this mindset is totally corrosive to a functioning society.
It's almost a human universal that existing complex systems are frustrating to ideologues who don't yet understand how anything works but have big dreams of radical transformation to match their own imagination and are then confronted by push-back from many directions. Criticizing complex systems is easy: they're always full of apparent (and real) inefficiencies, inconsistencies, etc. Understanding how they function and how they came about is a lot harder, requiring a capacity for nuance, humility, and years of effort.
In practice those slogans and jokes turned out to be smokescreen for a massive grift, privatizing previously public institutions and resources to the benefit of a few close buddies, shredding labor rights, institutionalizing more overt and personally profitable forms of corruption, dismantling or undermining all sorts of systems set up to protect people from harm, and generally undermining the social fabric for the benefit of the wealthy.
By all means, watch and enjoy the show. Just don't take it too literally or base your public policy on it.
As an American leftist, I never thought the show was particularly Thatcherite. Just as often some nitwit politician wants something dumb to win a by-election and the civil service has to save the day. Sir Humphrey is just as often the hero as the villain.
So in a sense what you say is true, there’s not really enough to bad your public policy on. You just learn everyone is self-interested sometimes, and institutional inertia is real.
I've watched this happen in the governments of four other countries I've lived in. It's largely the same story regardless of who's in charge (left, right, green, libertarian, etc).
Try to build institutions? Something backfires.
Try to tear down institutions? Something backfires.
Try to do the right thing? Something backfires.
Try to do a favor for your buddies? Something backfires.
That high politics are a complicated, nuanced dance between powerful agents and tidal forces is not under question, nor is the fact that the system generally works (obviously - we're still here and doing alright).
But that doesn't mean that you don't encounter some rather absurd situations the higher the station (which is the point of the show).
As I said before, it's a comedy, not a political science thesis. It can no more prescribe a remedy than could a rant at your local comedy club. That's not what it's for, and never has been. If you start basing policy off a TV show, you've got problems.
