The headline argument hinges on the size of infinities to assert that you'll run out of goals to live for eventually, and thus will eventually become vacuous and despondent over an infinite timeline. But this reliance on infinities is also why they cannot propose a concrete age limit for the Logan's Run Law their gut so desires. May that remain the case for infinity.

Some counter-shower-thoughts:

Are children's lives vacuous and despondent? They have no sense of mortality, no sense of limits, no comprehension even of the fleeting nature of their childhood, and honestly they aren't really striving for a goal the way an Everest climber, or even the average salaried worker, is. Maybe there's more to the meaning of life than striving towards a lofty-yet-grounded-and-pinpoint goal?

Are dogs and cats given longer legal lifespans than humans because they seem happy enough without this vaunted sense of mortality and strife?

Why are Everest summiters or retirees left without goals to strive for, when they've only achieved one or less? That's tangential to Williams' proposition! Is it not because they have too little time left before their "dead"line to forge and pursue a new one, particularly given the toll of aging on mind and body? That seems like the opposite of the point the author's trying to prove.