Compulsory vaccination is undesirable and damn near impossible in any civilised society - full stop.
But you don't need the Government to impose restrictions in order to improve vaccine take-up - market forces and the reaction of businesses to them will do the job quite well.
I wouldn't want to be in the confined environment of a full aeroplane with even a few refuseniks on board - so any airline that requires proof of vaccination will get my business - and that of many others too. Watch QANTAS in the next few weeks to see how airlines will start to require vaccine data as well as negative tests.
On a more prosaic level, if I'd had the vaccine and Aldi had a 'vaccinated shoppers only' policy for certain hours/days, then I'd shop at those times - if that was so popular that it expanded and pushed the unvaccinated into a few unsocial slots, then that is market forces, my friend ...