I'm not saying I necessarily disagree that "a small accountable republic driven to progress only on issues where there was minimal to no opposition" is desirable today, but you have put forward no valid argument for it.
For instance: they foresaw the problems powerful interests acting in bad faith could cause, and so we now enjoy judicial recourse when politicians or appointees make arbitrary, capricious, or corrupt decisions. The fact that we're discussing legal challenges to the FCC's decision as even a possibility underscores this point.
We understand more about human psychology / neurobiology now, of course, so this is one limitation of uncritically accepting their advice. We also have the benefit of over two centuries of additional hindsight. Still, I think there is good reason to at least consider the opinions of people who would, by any reasonable reckoning, count as political systems design experts of their time.
Many countries such as the UK have legally enforceable limits to the amounts parties can spend on elections. This helps, the UK government is not totally in the packet of big business. The only celebratory I can think of having been elected is Glenda Jackson. Of course big business still owns most of the "popular press".
How about we make these people complete a PhD in three different fields. After that, they will be humbled enough to be fit for politics. (Of course, experimentation needed for validation of this claim; anecdotal: Merkel has a PhD and she did pretty well so far).
Going back to such a system would require incredible tolerance on both "conservative" and "progressive" sides. We would have to accept that within one nation there would be other states regulated in highly different fashions than our own.
What we need is systems themselves that take human nature into mind. The founding fathers of the US set out to create this exact sort of system. And they really did. Lacking a super majority, literally a single senator can prevent a political appointment. So on this issue, if the senate really did not want to put into appointee into the FCC who was in favor of dismantling net neutrality - they had that power. When Pai was appointed by Obama in 2012 his views were no secret. The senate could have said no. McConnell could have proposed a new person, Obama formally nominates him, and again the senate could reject. They are under 0 obligation to approve any nominee - ever.
Yes, this would be incredibly dysfunctional - but that is precisely how the US government was envisioned. The whole checks and balances thing we learn about in elementary social studies is specifically about preventing something from happening unless there is mass consensus. The founding fathers did not want a huge, powerful democratic government - they wanted a small accountable republic driven to progress only on issues where there was minimal to no opposition.
You can even see this in things like the bill of rights. The bill of rights does not, for instance, guarantee you the right to free speech. It says you already inherently have that right - it is inalienable. The bill of rights does not grant you a right - it prevents the government from infringing on your natural rights. In other words the view is that governments cannot grant rights, but they can take them away. A dysfunctional government maximizes the freedom of the people by preventing the infringement of such freedom except in cases such that there is a mass consensus of its merit.
The problem is that the doomsday scenario of all of congress falling into one clique happened. Politicians all need money to get elected and stay in office. Corporate donors (and influence) is where that money comes from. And this is where I think the problem is. But I also don't think there's any solution to it. Imagine you take all money out of political campaigns. That don't stop already famous individuals from running for office and their advantage in these cases would be monumental. There are radical ideas like treating political duty the same as jury duty, but I'm unsure how well that would be publicly received.
The point here is that I don't think 'just get better politicians' is something that's necessarily workable in the longrun. We need to create systems that readily accept the realities of corruption, cronyism, and general pettiness -- but then operate in a publicly desirable way regardless of this.