The OP needs to check their local regulations!
Of course they do! But you were the one claiming that even major vendors like Digikey or Mouser "wouldn't have paperwork in order" with regards to country standards where they are selling their goods, which I, frankly, find completely ridiculous.
Provide evidence to back your claims please that Digikey and Mouser submit each of their likely 1000+ power supplies for Australian testing and approval? 
Provide evidence that they don't? You are making that claim, not me.
Digikey, Mouser, Aliexpress, Evilbay etc all sell power supplies some are good and some are bad and if they have not gone through the local approvals process prior to being resold in Australia they are not legally supposed to be sold. If a product that uses mains power in this country uses a brick type supply internally sourced from elsewhere in the world then that product overall needs to be approved not the brick.
If you are conflating Mouser (which has an Australian subsidiary and operates thus according to the local law) with individual imports from AliExpress and eBay, I think it is you who needs to get some more information on the subject, not me.
I doubt that the EU is dissimilar for approvals prior to dropping their mark on a power supply or mains product but I haven't looked and wouldn't make statements claiming that knowledge,
EU doesn't "drop their mark". CE is self-certified - i.e. you as the manufacturer or importer affix that marking on the gadget you are selling and you are responsible for providing any paperwork that the device is compliant with the relevant norms should anything happen (declaration of conformity + anything needed to back it up - typically results of lab testing). And I can pretty much guarantee you that any of the large vendors or importers have at least the declaration of conformity on file and available on demand (it is not their job to do ensure the certification itself but they have to have the paperwork from the manufacturer), otherwise they would have been fined into oblivion and their products banned from being sold.
This is how it looks for a Mouser sold MeanWell charger, for ex:
https://www.mouser.com/catalog/additional/MW_PB-300P,360P-CE-dec.pdfOr switching power supplies (also MeanWell):
https://www.mouser.com/catalog/additional/MW_GSM40,60A-CE-dec.pdfYour statements are ridiculous and WRONG and again the OP needs to check locally to make sure his ass is covered.
You are completely missing my point. Again.
Of course they need to check locally.
BUT if they buy a brand name supply from a
reputable vendor (i.e.
specifically not eBay or AliExpress) that is
operating in their country, such as Mouser, Digikey or others (
not individual import e.g. from the US Mouser!), then they have pretty good chances that the product will be compliant and fine because that vendor would otherwise be unable to sell it there. I can't see a specialist distributor like Mouser or Digikey risking their reputation and business on selling stuff that is not legal to sell in the given market due to lacking certification - they would be exposing themselves to huge liabilities should anything happen.
If you want to claim that Mouser is selling stuff that is not legal to sell in the country because it doesn't have the paperwork in order (whether it needs to be retested by a local authority or not is not relevant - that's not the buyer's problem), then you better provide some better evidence than just calling something "ridiculous and WRONG".