In the long run, the only stable population shape ultimately is a column that is thicker at the base.
AFAIK you are correct.
Let me elaborate on this. Infinite growth Capitalism combined with technological development leads to a civilization whose citizens are constantly concerned with more, a nicer way to say this is growth. This in essence means greater and greater levels of consumption. Their entire existence, their brains, are wired for this hit from growth and progress. Buying a new phone, a new car, new clothes, promotions, salary increases, bigger houses, longer vacations, more sexual partners, etc. They are looking to constantly grow. Without that hit, they would very quickly become dejected and depressed.
But this all comes at a great cost. For one thing, people living for that hit don't live in the present, they are always oriented in the future giving up their entire present for a promise of a greater future which never comes, all they get is a hit along the way to that future and anticipation of next hit motivates them. And it's possible to have a psychology that is not set up to constantly seek this sort of hit. Therefore, for a person living with infinite growth capitalism, the transition is probably highly undesirable.