> I believe that once we reach a post-scarcity phase of civilization
That may never happen.
> the attention of other human beings will be the last, zero-sum scarce resource
It doesn't have to wait for it to be last for that battle to get underway.
> And the competition over it will be no less intense and brutal than historical conflicts over the basics of life
Depending on where you live, you may already be there. It's the downside of the future not being equally distributed, you also get the downsides of that future early.