That's how it happens in the US too: the representatives of the people confirm Supreme Court justices.

However, I suspect you are implying that those representatives are not representative of the overall population. I don't believe that our constitution stipulates that they will or should be; it quite explicitly lays out a system where majority rule doesn't carry the day. I admit I'm deeply suspicious of arguments that advance the notion of majoritarianism, especially from progressives who seem to think that it's inevitable that they will remain in power forever. However, I think there are indeed structural problems with representation in congress; the House, at least, should have many more seats (there are pragmatic problems to be solved along that path, but we could solve them if we chose to do so) so that each member is far more accountable to a much smaller group of voters. However the founders of the country made the Senate explicitly representative of the states and not the populace as a whole. While a big part of the specific historical reason that was done (to protect slave states' power so they would actually sign on) was a horrific injustice, the reasons behind doing so (to ensure that the federal government was accountable to the states, so that states with large populations couldn't simply run roughshod over those with smaller populations -- a check on federal power) seem to me to hold some value. So on contentious and narrowly-decided issues, majorities cannot simply dictate. Perhaps our current dysfunction deserves re-evaluating some of those ideas, but I've yet to see a compelling argument that requires we undo this basic function. The fact that our parties cannot figure out how to compromise or moderate themselves to accomplish lesser deeds of significant value does mean the system is broken.

As for what all other western democracies may do, I don't think popularity is the best argument in favor of any policy or system. I could be swayed by an argument that their methods are better, but I'd have to see the argument.