Just for some points of reference:
1)
Healthcare: Denmark covers costs for Greenlandic patients needing specialized treatment in Danish hospitals. Universal Healthcare coverage
2)
Danish Commonwealth Welfare: Greenlanders benefit from the broader Danish Commonwealth system, including access to Danish social assistance, housing allowances, and pensions.
3)
Education: Greenlandic students get grants and support to study in Denmark, reducing dropout rates and fostering skills.
3A) For Greenlanders studying in Denmark, higher education is generally
free, as Greenland is part of the Kingdom of Denmark, granting citizens the same rights as Danes, including tuition fee exemption at public universities, but you must cover living expenses (around 5,000 DKK/month) and potentially some program-specific fees. Some exchange programs or specific non-EU/EEA agreements may have different costs, but generally, if you hold a Danish/Greenlandic residence permit, it's free
4) Danish citizenship (which they all have) offers access to the broader Nordic welfare system (social security, education grants) and opportunities for Greenlanders to study and work in Denmark and the rest of the EU.
So, let's say each Greenlander got 10,000 USD, tax free, regardless of their age. Looking at the above things, how soon would that 10,000 be eaten up by the newly additional costs of each person in Greenland having to purchase/pay for their individual health care? What about higher education costs? How far would that 10,000$ go towards a 4yr public (not a private university) university, meaning a Greenlander is treated the same in say that state of Connecticut to attend the University of Connecticut which is 'subsidized' for residents of Connecticut vs someone from say New Jersey attending - answer, 1 semester, that's it.
The payment of 10,000 USD is bloody peanuts to the average Greenlander in terms of what their new expenses would be. Please don't tell me that Greenlanders would be able to continue with their Universal Health Care coverage and free higher education because the people of Puerto Rico or Samoa don't.