H1-B and L1 can actually be done in-country, but for some reading going abroad and get consular processing has a lower chance of RFE.
US is unique in that the visa sticker and your right to remain in the country (status) are two different things. The only purpose of the visa sticker is to allow you to travel to a U.S. port of entry, where you apply for admission, and therefore legal status. You can have legal status in the U.S. while the visa sticker has expired, and your status can be changed or extended domestically. However unless you have a valid sticker you cannot leave and return.
For non-PR, I don't think Australia distinguishes visa and status like US (i.e. you can't have valid status while your visa expired)
There are some technicalities -- your passport has to carry the re-entry permit, but it's affixed to everyone who requests it at the port of exit, granted it's up to 1 yr.
Prior to the mid 00s you could renew at any consulate but they changed it so you could only renew in your home country.
The recent policy change ended that possibility altogether.
(You might have known that, but I thought it's worth clarifying).