The left does not want people hooked on benefits. Paying benefits is expensive in a socialist society. The left wants workers who are properly compensated in line with the value they provide, and a social safety net for when they are unable to work.

You could say that the leadership of the right is desperate for immigration and to get people on benefits. Immigration gives nativists someone to look down on, making them easier to exploit. Paying sub-poverty-level benefits is cheap and makes the workforce desperate to accept just-about-poverty-level wages. The working class exists in order to frighten the middle class. The underclass exists to frighten the working class.

Also bear in mind that illegal immigrants do not get "hooked on benefits", they get deported or exploited by "economic libertarians".