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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)
The proportion of senior public sector roles which are filled on an "interim" basis, often for years by contractors on sky high day rates far in excess of what they are allowed to pay a permanent hire is a complete scandal in general.
Partly the far below market rates offered for such roles but also the tolerance for mediocre contractors just occupying a seat (or not even that in your example)