Your argument ignores the fact that people do not "need" to demand a full market wage if they already get UBI. Indeed, it is often claimed that state subsidies to the poor are in effect subsidies to their employers.

The situation exists where any low income person gets subsidies from the state, e.g. through cheaper housing, free schools and healthcare, etc. People are still incentivized to work even when they get these subsidies. UBI merely extends such subsidies to include food and other daily expenses.