Social Security and Medicare are both very popular with those receiving them and both very efficient with very little overhead. Soc Sec has an admin overhead of less than 1%. Medicare's overhead is 2%. The overhead of private healthcare is on average 12%.
As for what Medicare covers, again those who have it love it, and it can be compared to Silver and even Gold plans as rated by the ACA market exchanges.
Meanwhile, UBI is meant to replace over 100 government programs (but not Medicaid/Medicare), and over 100 tax credits to simplify the tax code. Why give someone $3000 off their taxes for owning a house if they are getting $12000 cash from UBI?
The net increase in taxes required for UBI is not as large as you seem to think it is. In fact, it would be a reduction in tax burdens for 8 out of 10 households, which likely includes you. If your taxes go up $7000 to pay for $12000 in UBI, that's a net gain of $5000 and thus a net tax reduction equivalent to a $5000 tax credit.
RE: Will universal basic income give too much power to whomever distributes it?