That's the most reasonable way to do it assuming you are financing primarily out of income taxes.
If it is done this way (i.e., completely taxed out at moderate or high income and/or is income-dependent), then it is no different from current welfare and social assistance programs. IMHO, the attractiveness of UBI is low administration costs (however, it will lead to a new problem of many government employees losing their jobs). In addition, to be successful, it should not alter the employment decision much (like current welfare does with 50% effective marginal tax on each $1 earned above some low threshold).
While I am not sure we can afford it, I am sure that no left-wing government would be willing to introduce it to replace all the existing government social support system because it will lose the control over the distribution of the large portion of tax revenue and we all know how liberals love to have control over our money.