Not really. Again, you are making several misconceptions (this isn't uncommon, economists don't really understand finance and they understand even less about financial history so they say very odd things that ppl seem to pick up on).

First, the system was not safe...at all. There were pretty much constant financial crises through the 1960s.

Second, the reason why these crises occurred is because the US promised to buy central bank gold at X price. This wasn't sustainable, this caused crises as central banks tried to acquire gold and the UK/US tried to stop them doing so (gold pooling arrangements are an example). It was a fundamentally bad system.

Third, the reason why the system appeared "safe", in today's terms, was govt assumed all the financial risk. Trade and capital accounts were closed, even ones that were open had significant limitations. For the US, this didn't work out terribly because they could keep printing "gold" paper that actually had no value...for everyone else, it was terrible (particularly, the UK). This required some level of protection of domestic industry and resulted in poor competitiveness, high taxes, and high prices for consumers. The funniest thing about this re imagining of the 1960s is that if you actually read what policy makers thought, they believed it was terrible system that would fail (and they were correct).

It is impossible to distinguish between productive and speculative finance, and it is actually very important that you don't try to (this was a major concern in the 1960s and for the IMF, they believed they could control speculative capital movements distinct from productive capital movements...it didn't work). The 19th century saw several financial manias, they produced waste but also tremendous value (canals, railways, electricity, etc.). You can't have one without the other. Finance is risk, and you can't take risk without the possibility of failure.

One of the problems today, typically outside of the US, has been the inability to cope with failure (and so you get lots of idiots saying we just need to get rid of "speculation"). No, the aim of capitalism is to maximise productivity/competitiveness by maximising failure. The solution to this problem is social policy (i.e. Denmark) not trying to fiddle with capitalism. It should be no surprise that this viewpoint has coincided with an increase in concentration of wealth (rich people generally don't like competition/capitalism...another aspect of history that is forgotten).