Why are government benefits considered taxable income, and why is the recipient required to pay the tax rather than have the tax subtracted from the benefits upfront?
Which benefits?
In the case of Social Security, if you believe that because of other income your benefits will be taxable, you can arrange to have income tax withheld from them. Similarly, you can opt to have income tax withheld from your unemployment benefits when you receive them.
In the case of unemployment, it is intended as a substitute for wages, and the tax that pays for them is not (except in a few states) paid in any part by the employee, but the employer. As a general rule, any sort of government benefit that is intended as a substitute for income the person would have received if the economy and/or weather had gone as they hoped is treated as income for purposes of taxation. (SSI is not considered an income substitute since a person qualifying for SSI both cannot have been capable of earning income and can't have assets of their own that would earn income.)
In the case of Social Security, making it potentially taxable was enacted in 1984, and increased in 1993, as a substitute for making Social Security benefits means-tested.