Consider this. The maximum possible pay Person Y can obtain in the current market is $20 per hour. However, cutting unemployment pressures this Person to get a $15 per hour job immediately.
For the sake of the argument lets assume that unemployment benefits give $15 per hour. Those $15/h represent $15/h of pure waste because they have to be paid by employed people.
However, someone using unemployment benefits to obtain the $20/h job implies that taking the $15/h job wastes $5/h of your potential and unemployment increases your future potential by $5/h.
Those $5/h are pure waste, nobody gets them, not even your boss because an employee working in a fast food restaurant can generate less economic value than an employee in a warehouse.
However, unemployment generally lasts as long as necessary. Only a handful of individuals live on unemployment benefits over the long term. If you are unemployed for 6 months you cost the state $14400 (assuming $600 in benefits per week and 4 weeks per month for simplicity). It takes $14400/$5/h = 2880 hours of the warehouse job to break even from a macro economic perspective or 1.6 years with 1800 working hours per year. Of course this is not the actual tax revenue, assuming 27% of GDP is evenly taxed it would take 6 years to break even for the government.
This is just a potential benefit from the "unemployment benefits cause a worker shortage" perspective. If you go one step further there are even more situations in which unemployment benefits can help the economy. For example, what if those people will stay unemployed anyway, even if you cut benefits? They still buy products and services that generate business revenue and the business can use the additional money to hire previously unemployed people.
Of course the ultimate underlying assumption behind everything I wrote is that the economy has an abundance of goods and high inequality. None of this would work in an economy with long term scarcity like a developing country. As it is right now, full employment in the US is a "bonus", the economy doesn't depend on it. Other countries are willing to do almost everything the USA can do but they do it cheaper, which negates the need for low skill jobs to be done in the US.