I'd personally even take it one step further: those who are payed the least need benefits the most. By relegating this work to temporary workers you're doing exactly the opposite: cutting away the privileges that the full-time employees have. Not to just one employee, but anyone who's ever going to fill out that position.
A trip to the doctor would not make a dent in a senior engineer's pocket (regardless of the insurance), but a janitor could not afford a trip to the doctor in the first place. This could work in a country with good social programs to fall back on, but it has catastrophic consequences in the US.