That is the idea that, in Britain, entities like the NHS and the BBC have operated under. Charters specify the responsibilties and duties, and guarantee the funding needed to provide these, but the organisation is (supposed) to carry these out wholly independently of the government of the day.
It actually worked quite well for some time, but has been under increasing pressure and subject to increasing government sabotage over the past 20-25 years.
It's also the idea behind science/engineering research funding bodies the world over. These should direct funding for grant proposals not on political whim or popularity but on the basis of what is actually needed. Again, though, it does get sabotaged a fair bit.
Exactly how you'd mitigate this is unclear, many governments have - after all - the leading talent in manipulation, corruption, and kickbacks. But presumably, strategies can be devised to weaken political influence.