I'm not really arguing for or against direct representation as such. I tend to judge democratic systems by their practical effects. Do they result in governments that act with popular support? Are the individuals who achieve power within those governments accountable to the people they supposedly act for, such that there will be consequences for them personally if they don't faithfully act for the people and do a decent job of it?
It's true that directly elected representatives are, in some situations, more likely to meet those standards. Indirectly elected officials are, by the nature of the system, not in need of a personal popular mandate to achieve power, nor directly accountable to the people, and the gap widens as more levels of indirection separate the official from someone who actually had to win a popular vote.
But I'm not necessarily arguing for directly electing everyone in public office. I don't think that works very well in practice either, because voters get election fatigue and anything but the big ticket elections can easily end up being more about which candidates have the best PR and spin rather than the best policies on the issues.
What I do think would be a big improvement in many cases is directly electing the people at the top of a system of government and having appointed officials subordinate to them. Many of the democratic deficits identified in this discussion, from forming the European Commission to choosing the PM and by extension the government in the UK, are examples where the lower level representatives are the only ones who actually have to win an election, and then some number of averages of averages up the tree you get the people with most of the real power being isolated from needing to attract or maintain popular support. I don't think this kind of arrangement is healthy for democracy, and I think forcing direct elections for those most senior positions would go some way to fixing the problem.