For me the main argument is, storing every transaction on the main chain requires servers in a data centre.
This means it's going to be run by a company and therefore subject to local government whims and can be shut down.
Ironically, even VISA face this, they only keep transactions for around 6 - 12 months. Keeping them longer would require enormous storage and data costs.
They lost a battle with, I believe the EU, who wanted them to keep records for longer as part of AML, which is why VISA fees are rising.