Immigrants are a) not a financial burden long term, people might need assistance at first but will generally get established and then pay into social programs and b) the US is incredibly wealthy. We can spend trillions on the military, we can afford welfare.
The point about east germnay was that it inhibited freedom of movement. I see no practical difference between preventing someone from leaving and preventing someone from entering. Both deny the person their freedom to live where they choose.
The point about colonialism is that colonialism is the reason much of the global south is in cycles of war and poverty (eg, european powers dividing up africa ignoring tribal boundaries). so it's pretty rich to extract wealth from a place to build your indsutrial economy, and then tell people trying to escape that war and poverty that they aren't allowed the fruits of that wealth extraction. and why are you pretending this is ancient history? the french were comitting war crimes in algeria against the independence movement in the 60's!!
automation is coming. expanded welfare will be necessary regardless -- we cannot have a world of 10 billion programmers and service workers. the top strata owns the vast majority of the world's wealth. if we returned to 50s era tax rates these people could still live extremely opulently and we would have morw than enough resources for all americans and immigrants.