It's actually super easy to do. See, you just...make sure that rather than cliffs, you have percentage based reduction of benefits. I.e., you lose $1 of benefit for every $2 you make, or whatever. And something similar with assets (though admittedly the details would be trickier to avoid it being gamed).

Neither the group that needs help (and their supporters), nor the group that doesn't want to give hands out to people who refuse to work but could, have reason to object to something like that.

The actual problem is the red meat that welfare/socialism is to our political bases in the US, and the incentives of politicians, on both sides of the aisle, to ensure it persists. If you do the obvious thing to actually address the problem, neither side can use it any longer to stir up the base. So the incentive is to not actually fix it.