It's possible, I think. I just took a look at Commsec (one of the big Australian brokers) - they ask for your citizenship, residency, and tax residency, so they certainly cater for foreign accounts. On the other hand, they ask for an Australian residential address, so I don't know if they allow you to open an account from overseas.
I had a chat with one of the big 4. You don't have to be a resident, but you have to identify yourself in person to open a regular bank account or a trading account. The regular account can be opened from overseas and you can make deposits, but you can only access your funds after you have identified yourself in person at a branch.
Depending upon the time of year, a trip to AU could be an inconvenience. But if my super strong USD and super weak commodity country stock markets and currencies happens, the inconvenience will be offset my the benefits.
Do you want an Aussie brokerage account or just to buy Australian companies? If so, why not use your local account or something like Boom HK?
I would like to buy stocks of world class companies that are based in commodity countries. My preference is to buy them locally and avoid the foreign dividend withholding. I anticipate moving outside the US upon retiring and I would keep a US account for social security deposits. But, I may want to move my financial assets out of the US. Add to that my desire to hold undervalued foreign stocks and my desire to avoid the ever increasing US restrictions on banking accounts. Having foreign brokerage account(s), seems like the logical thing to accomplish those objectives. Thanks for the mention of Boom HK. I am not familiar with them, but I will look into the company.