To be fair, Switzerland comes very close. The public can pass initiatives or constitutional amendments without government intervention through public votes, and the few Swiss people I know consider this to be the primary political system in Switzerland (not the representative electoral system they have, though they also have a very interesting mechanism for their President which requires cross-party agreement for any government decision).
Saying "no system fully implements direct democracy" feels like a no-true-scotsman stance, since by the same token no system fully implements representative democracy either (AFAIK no country guarantees that there is a precise percentage match of party representation to the popular vote with no lower bound on how many votes a party needs to enter, as it would be unworkable to have such a system).
> The problem is “the people” don’t have a single coherent group consciousness capable of reconciling competing priorities. That’s what leaders are for.
The flip side is that in representative democracies (especially with broken voting systems that are not even remotely representative such as in the US, UK, and most of the world) you are very limited in your choices of leader and thus sentiments which are popular with the public can be completely ignored. There is no mechanism to force a public initiative that has legal weight, so you have to hope that a major party will be in favour of your pet issue and they can convince other bureaucrats to support something that is popular.
I would not say that I'm a proponent of direct democracy but I don't think having some public initiative system would be a bad thing. But if we are going to keep representative democracies with the argument that the leaders represent the people but have some expertise (though cynical people would argue that is not the case anyway) then you cannot have broken electoral systems because their political power is no longer morally justified. But of course, no party that gets in power would likely ever change the entire electoral system since they have a strong political incentive to not do so (and with representative democracies, election promises aren't worth the paper they're written on).