I can't claim to have reviewed every one of the 60 odd national governments with Senates, but in my review of a large number I find that limitations similar to what I outlined for Australia's Senate are the norm, not the exception.
Canadians probably have a skewed view based on our proximity and shared media with the US, but the US Senate as the most powerful legislative body is really exceptional (I know this is a debatable claim, I made the argument at length here, but in short form the special powers unique to the US Senate are better powers than the ones given to the House). A few other countries (Brazil, Italy) have equal senates, but looking at France, Germany, Australia, the UK, Japan, India, Indonesia, Mexico and Spain you consistently find Senates that have significantly reduced powers as compared to the lower chambers of these legislatures.
We'd be fools not to learn from this. The US Senate is derisively known as the "place good bills go to die" and Italy is infamous for "50 elections in 50 years" after World War Two. Maybe it works well enough in Brazil, but even by having an upper chamber we are in the world democratic organizational minority and by empowering our Senate to be equal to our House in scope of powers, with no ability for override, we would be in a very exclusive club of unenviable systems. It would be a radical experiment.