Can't help myself sometimes. As a codicil to the above, it's not just about how much a country spends on sport, it's about how it spends it. Some of the discussion of UK's improvement over the last 12 years has talked about how they've spent the money to get the best coaches from around the world into their elite programs. They've taken a strategic approach to junior development by investing in coaching capability and talent ID at lower levels of sports. In Australia, we've closed the AIS residential programs and scattered the associated sports science and talent development functions. Was that a good decision? I'm not sure, but it doesn't look like it.
The UK and Europe are full of countries with high population densities and small travelling distances. They can operate multiple, decentralised high performance programs that create critical mass through geographic nearness. They can learn from each other through intra continental competitions and conferences, far more easily and cheaply than Australian coaches, athletes and sports can.
Frankly, Australia has punched above its weight internationally for years, because we spend more on sport (as per my post above). Once other nations with similar or better economic capacity decided to spend more of that capacity on sport, we were always going to slip down the rankings.
Add to that the '1 in a million' athletes in various individual sports (Ian Thorpe, Eric Heiden, Michael Phelps, Nadia Comaneci, Simone Byles, Usain Bolt, Paavo Nuurmi, Carl Lewis, Chris Hoy, Wu Minxia, Ahn-Hyun Soo). These athletes pop up in sports where they have multiple events at international competitions (speed skating, gymnastics, swimming, diving, track cycling, sprinting, distance running) and are able to collect multiple titles at events. They inflate a country's apparent sporting success significantly. 3 athletes - Ledecky, Phelps and Byles were responsible for almost a third of the USA's gold medals at Rio (13/46).
These '1 in a million' athletes are more likely to occur in countries with large populations and sports where they can win multiple events in a single competition. So they're perfromacnes count more to a country's medal count than a whole team's performance in soccer, basketball, etc.
China, USA, India, Indonesia, etc. all are likely to have more of these potential champions floating around in their populations than is Australia. To the extent a country's economy and sporting system supports these athletes' realising their full potential - while avoiding debilitating injury and burn-out - they're able to use them to improve the country's sporting performance internationally. So China can dominate diving every Olympics, with different, teenage divers each time. The USA regularly produces dominant individuals who each win multiple medals in a single sport.
So Australia has a history too of '1 in a million' athletes in these multiple event sports at international competitions but they're not regularly produced - Cuthbert, Rose, Gould, Thorpe, maybe Klim then I'm struggling. It certainly isn't as frequent as for larger countries. USA usually can produce at least one such athlete every 4 years and, as above, China (and Russia) can as well.
There are around 50 countries with larger populations to draw from than Australia. Only two (USA and Saudi Arabia) have a higher economic capacity (GDP per capita) through which to fund national sporting programsperformance. If those other 48 or so get up there economically, it'll be that much harder for Australia to outperform them. The relative performances of Australia and UK in Rio demonstrates that reality.