Meanwhile here in italy when a major company fails and goes bankrupt because of shitty management, corruption and greed, we first "save" it with public funds, then sell it to someone else to profit off of it

A massive corporation going out of business sucks in the short term: people lose their jobs, among other financial woes. But if you keep bailing out failing corporations, you harm your economy in the long run because you're keeping a company artificially on life support using budget funds. The company will continue to fail and lose money, setting your country back years in terms of productivity and innovation, and your economy will fold inwards.

Property developers in China, unlike banks in the US, are not the backstop of the economy. They are not too big to fall: it's just that their distressed assets need to be managed to minimize losses to their customers.