In my vague and ill-informed opinion, the key to fixing democracy is to have most people involved in real decision making, most of the time.  Those not currently involved in decision making should instead be involved in some sort of political party, activist group, movement, or whatever.  This would only work if it was seen as a valuable responsibility and privilege of citizenship, and participation in politics a necessary public service, rather than a burdensome annoyance loved only by a bizarre and fanatical minority.

This sort of system would need some rather serious devolution of power to work, or the breakup of modern nation states into many, many micro-states.  The problems of that are well known, and furthermore there are many problems both prosaic (traffic management and land use) and extraordinary (war) which need organization at a higher level.  Further, business and whatnot works better with fewer distinct sets of laws, not more.  So there's those problems.

But without some sort of mass involvement in politics, on a regular and sustained basis, there simply isn't a counterweight to the loud and greedy rich.  Well, I suppose you could use law to prevent their existence to begin with, but I'm already well into utopian speculation, so . . .