Why the heck do invaders face jail time? They should be sent back home, with their children.
While costly it serves at a greater deterrent rather than toss them back across the border to try again the next day.
The desire for American freebies is great we have to make fear of capture and consequences Greater.
Because our borders are still so porous that they can try, try again to cross again with a decent chance of escaping detection and reaching the land of welfare and honey.
If the only penalty for breaking in is removal and a chance to try again, the disincentive isn't strong enough. Ideally, with a strong border (Wall plus patrol), we could do as you suggest.