The government gives lots of people lots of benefits. Suggesting they should exclude kollel families from entitlements to which everyone is entitled would be very unconstitutional. American law is very big in treating everyone equally.
As to the question about whether the government should aid persons who are poor, regardless of reason, that goes back. Originally the policy was very restricted. One couldn’t get “welfare” unless you had sold all your possessions, and moved to the “poor house”. It was felt that giving money to poor people would make them lazy and corrupt their souls. For the most part, “welfare” was considered the function of private (usually religious) groups.
As America became “diverse” (this goes back 250 years, originally America was dominated by WASPs), the newcomers tended to be Jews and Catholics whose traditions supported charity, and overtime the government got into “welfare” business and at this point, add to the poor is considered by most Americans to be a proper government function, so we have programs such as welfare, food stamps, WIC, social security, medicare, CHIP, tuition waivers at universities, legal aid, Obamacare, etc. This isn’t really controversial anymore, and no one wants to go back to the old system which saw support the poor as being a bad thing. This has proven very good for frum Jews since we have large families and many people who put Torah and Mitsvos ahead of earning a parnassah, and consequently benefit from government hand-outs.
And yes, one can argue they got much of the idea from Yidden (directly or indirectly). Our communities always tried to be a welfare state (which was very hard for financial and economic reasons).