Volunteers are not relevant in this case as the problem was not lack of people to inject, but rather that the vials were stored in a refrigerator which did not have temperature monitoring.
According ABC News:
More than 120 doses of Pfizer's COVID-19 vaccine are thrown out after a possible storage error at nursing home in Melbourne.
www.abc.net.au
"The company has advised the federal government that 25 vials were left over and stored in a fridge." ... "Therefore, out of an abundance of caution, a medical decision was made not to use the remaining vials."
So it does not appear to be as you claim that none of the vials could be used, but that in fact some where used , but then the unused ones were then stored and as they could not verify that they had been stored at the right temperature had to be thrown out. IF they had adminstered more on the first day then 25 vials (up to 150 doses) were destroyed. This is very wasteful.
News.com (which is less reputable than ABC) also notes that there were extra unusedvials (and not the total supplied) - they actually claim the facility received double the doses they needed - so one has to ask rather to try and store the excess number, why didnt Aspen health contact someone to come and collect the excess delivery for deployment elsewhere?
www.9news.com.au
Age care facilities do not want random strangers on site as it is too risky to the health of the residents, and health risk to residents are not just from CV19.
Firstly volunteers wouldnt be totally random walk ins, they would be pre-registered, subject to phone screening to make sure no symptoms and asked to come in. The vaccines are being adminstered by contract staff (not the aged care workers) who could give these in a room (office, meeting room, reception room) or even outdoor area (vernadah or carpark) away from residents after all residents have had their shots - this is what happens in the USA.
With no community cases atm, there are no restrictions on visiting Aged Care facilities at this time in most states, so if not directly intercating or crossing paths with at risk residents or their staff the risk is low.
Also vials can be transported in ice a short distance to another public building - townhall, medical centre, hospital provided doen before the limit of out of super cold storage is reached.
You just need to think sensibly and laterally.