An interesting idea - but it has a few snags. I do not think that Government funding would sit comfortably with the start-up culture. Governments (and quasi governmental organisations) are required to be risk averse. Plus there are already a host of grants and similar available - although those come with all sorts of complexity and obligations.
How about a different approach? We currently have SBRI initiatives https://www.gov.uk/government/uploads/system/uploads/attachm... that expose a wealth of interesting challenges and match them with direct funding to seek solutions. The snag here is that while the SB in SBRI is supposed to stand for "small business" in fact there is no such restriction. So some SBRI style challenges restricted to micro businesses and start-ups could be the seed corn needed to get a lot of businesses off the ground and a lot of real world problems solved.
How about a different approach? We currently have SBRI initiatives https://www.gov.uk/government/uploads/system/uploads/attachm... that expose a wealth of interesting challenges and match them with direct funding to seek solutions. The snag here is that while the SB in SBRI is supposed to stand for "small business" in fact there is no such restriction. So some SBRI style challenges restricted to micro businesses and start-ups could be the seed corn needed to get a lot of businesses off the ground and a lot of real world problems solved.