Yes, I agree, as part of what makes this program appealing is its simplicity and its relatively un-leaky bucket. That is if I have $2000 available for Bob, it's still pretty damn close to $2000 by the time it reaches his account.
As you suggest, it's difficult to imagine this shoehorned in with the tangle of programs administered by multiple agencies.
It's too easy for someone to say "Group X needs additional support for Reason Y" and end up with something just as expensive and complex as what we have now. I know, because I've managed to bait people on both the left and the right into doing it for different values of X and Y.
By "correct implementation", I mean one that replaces all welfare, social security, and probably some parts of the tax code. Healthcare maybe you can get away with treating separately.
I don’t know enough about Kenya to say one way or the other.