Until it’s addressed, corruption will continue to block progress on every issue.
Parliamentary democracies always turn into rule by and for the well off in society. Even if you were to completely eliminate money from political campaigns, you are pretty much guaranteed to see an over representation of the well educated, charismatic manipulators, demagogues appealing to xenophobic and short-term thinking in the parliament. It's the reason why Cuba for instance doesn't allow political campaigns, and runs elections based on profiles of candidates. Major policy issues are then decided by referendums. The key for representative democracy actually working in the interests of the people is for the representatives to actually be representatives of the population. Running national popularity contests undermines this because then elections become a contest of who can work the media the best.
Funnily enough, before liberal republics, people understood that democracy meant rule by the common people and not merely voting. That's why the elites decried it as mob rule. They knew it was against their direct interests. Aristotle even once remarked that in a society where 2/3rds of the population is rich, if only the 1/3rds which was poor could vote, that would be a democracy (although he also thought democracy was bad, because then the poor would rule in their own interests). That's pretty much where the idea of a dictatorship of the proletariat comes from.
Corruption then is not a problem that a liberal republic can solve. That is because it is basically the key mechanism by which liberal elections function.
Exactly, and this is the whole problem with procedural democracy. The focus in the west is on ensuring that process that's been set up is followed faithfully as opposed to the outcomes this process produces.