Well are you sure that'll be enough ? The current govt types warn against not taking radical enough action. If you go to 100% govt employment like back in the days of the USSR, That outta do it ! The Soviets had lots of govt 'public make work projects', and plenty of demand for products . . . of course there wasn't anything they could buy, and the stuff that most slaves (oops - 'citizens') could wait in long lines all day for & get was total s*%#t. - - - That still didn't mean the elites in the Communist Party couldn't get the good stuff from overseas though.
Absolutely, I agree 100%. But market efficiency should not be considered when calculating GDP. Service sector jobs help by increasing the rate at which GDP grows...for example a plumber fixing a pipe will grow GDP by maintaining the pipe's high value...but he never actually produced any valuable commodity, therefore his income cannot be counted as a part of GDP. Nevertheless, his job is important because it increases the rate at which the factory can produce valuable commodities which do contribute to GDP. By using the plumber's income in the GDP calculation, you have actually counted his work twice: his income+the factory production rate.
You forgot to mention service sector jobs that contribute inefficiencies such as the legal profession, for example.