So… Once Iranian government falls.

I wouldn’t take that as a given.

So the US probably got handed off this hot potato because, if no western countries is doing it, China or Russia will come in and cause chaos later.

Is this a joke? Western imperialist states entering would create chaos, while China and/or Russia entering would be stabilizing. Iran, China, and Russia are major BRICS partners, and have shared regional security interests.

Who do you think organizes, funds, trains, and equips the various groups of Salafi jihadist terrorist groups that wreak havoc in Western and Central Asia? The United States, with some assistance from Israel and probably the UK. The US has wanted regime change in Iran ever since the puppet regime they installed in the US-orchestrated 1953 coup was overthrown in the 1978 revolution. The US has wanted to regain its imperialist control of Iran for the last 47 years.

Edit to add a primer: The blueprint of regime change operations How regime change happens in the 21st century with your consent