"Why we cannot swap one impermanent source of satisfaction for another, and continue doing so?"
The act of swapping one impermanent source for another... is also subject to impermanence. One can realize this with logic or simply look at the experience of those beings that have tried... ie., every sentient being in existence :)
Our very existence is a cause and condition for the suffering of others. The First Noble truth contains both coarse and subtle understandings of Dhukka. The most subtle is what is called the Sankhara-dukkha. This is an all pervasive unsatisfactoriness. Swapping from one impermanent source of satisfaction for another is itself unsatisfactory. To recognize this as Dhukka is wisdom.
"For example, one might take drug A to induce euphoria, then when drug A wears off, replace it by drug B, and so on."
What will that experience of it wearing off feel like? Satisfactory? What about when all the drugs run out? What will be the karma of someone acting in this manner? Look at the very real experiences of your fellow sentient beings that have tried this... do you find them satisfactory? If not, why not?
Ice cream is my favorite thing to eat. I now regard it as a form of suffering. To really understand the predicament we are in we have to see the Dhukka in those things we typically find "happiness" in. All of this, no manner how many drugs we take, is subject to aging, sickness and death. That's Dhukka.