The 'cosmetically perfect robot fantasy' has no rhythm, it is straight line progressions, very un-natural. On the other hand don't let those weeds flower and seed, one plant can produce hundreds of seeds. If they are the same weeds we have the other thing they can do is after being pulled up and chucked on the compost they will flower and set seed which will sit there in the compost until you spread it.
My feeling is that those weeds are going to grow no matter what you do, and if you go "Oh, look at the lovely weeds, isn't nature wonderful?" nature, in the form of weeds, will take over. Nature is like that, beautiful, but totally ruthless, hoe regularly and keep it on a tight leash.