Packing an individual box takes minutes. So it's a question of capacity, and it's pretty binary. If they have enough capacity then a large majority of items can ship within a couple hours. If they don't have enough capacity then the 90th percentile shipping time becomes indefinite/never. A situation where packaging takes an extra day, end of story, is unlikely and unstable.

And I'd say that some robots are R&D, so not having money for them has no effect on shipping times, and the rest are a cost-saving measure, so they'll always have the money.

It's not like Amazon is running a zero sum balance sheet here. They have profits this could take out of and maintain all their service and speed.