You're right. They don't stop planes, nor boats and subs, nor tunnels. The Coast Guard can take care of the sea and I suspect technology can provide approaches for the rest.
As far as illegals not receiving social benefits, not all benefits are a result of social security. Education comes to mind. So does medical assistance. Increased services such as fire, police, erc. have to keep pace. Someone has to pay. While I don't discount the positive contributions to the overall economy, it comes at a cost. There's an info graphic at this
site that looks to estimate this cost by state.