But why does the time it takes to return to the government matter?
The importance of the money injected by the govt. into the economy by way of govt. spending is that it facilitates economic activity. That is the whole 'point' of money, it enables economic activity. For example, economists calculate that govt spending on the NHS has a multiplier effect of about 2.5 as it works its way through the economy. The Sankey diagram demonstrates how govt. spending enables economic activity. The time it takes to 'return' is immaterial.
Most of the money circulating in our economy originates from the government, either by direct govt. spending, or by the creation of money by the commercial banks for loans to businesses or individuals, under licence from the govt. Banks don't use depositors' money for loans, they create new money with every loan. This isn't figment of my imagination, this is what the Bank of England tells us.
Top of page 16 (for some reason my ipad won't copy and paste the relevant section)
www.bankofengland.co.uk/-/media/boe/files/quarterly-bulletin/2014/quarterly-bulletin-2014-q1.pdf
Money originating from the govt. makes up the greater part of our GDP. The rest comes from foreign earnings and investment. But let's not go down that rabbit hole. The point is that without govt. originated money we'd be stymied.