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Indeed it would, however there is a total lack of rational reasoning by the public here - you'd need to literally double the salary for software engineers in government, for example.
That's simply impossible to do when wages for other roles are so low - why should a nurse be on 1/4 the salary of someone who just types curly braces and aligns whitespace all day?
(hint: they shouldn't - there's a huge wage disparity which needs to be addressed, but the public sector is simply unable to follow the market for a range of nonsense reasons)
Paying a market rate for the permanent roles might help to fix this, I submit.