That depends entirely on the nature of the work.
Could you not suggest the same about voluntary work?
For example our local hospital has volunteers on the reception. They provide a nice welcome, point people in the right direction and if people need help they call the porters. They also have a nice coffee shop to direct people to.
What they don't do is book in appointments, manage the waiting rooms or process the paperwork. Although this bit is also mainly done on the reception it's done by people paid to work and who have contracts, training and the like.
If the volunteers on reception stopped turning up the hospital would be a less nice place but it would keep going; if the salaried people stopped turning up the place would be screwed. If the salaried were replaced by volunteers - as is occasionally threatened - then we'd lose the guarantee of an effective service.
Any time you're talking about filling 'mission critical' work with volunteers what you're effectively doing is looking for a free way of getting something done that should be paid for.