I'd probably allow anyone who was not working overseas for longer than a year to continue to draw it, its really about your permanent residence and where it is - on the other hand the number of americans who work abroad is astonishingly small - so probably not enough to worry about.
Part of what a GMI would need to overcome is ensuring that we have an accurate tracking program - a death should trigger an semi-automated removal from the rolls - as in you need to present yourself.
No system is foolproof, and even the best one in the world is going to have upwards of 2-3% fraud - that said the social security administration historically has been VERY good about tracking them down, and remarkably successful at clawing overpayments back.
In the end, by eliminating means testing you close down a ton of venues for fraud.
I agree, and that’s why I would never say it was virtually impossible to cheat one.