I think it is clear that Buddhism does not concern itself with capitalism, or any other economic “ism,” except to the extent that one should occupy oneself with a “right livelihood.”
And I want to point out that modern ‘capitalism’ bears little resemblance to Adam Smith’s use of the word. He had nothing good to say about corporations, and his use of the term “free trade” referred, not to to the ‘right’ of multinational corporations to move their capital freely around the world in search of cheaper labor pools, but rather to the right of each individual to freely move about to ply their trade. This is clearly not the case today.
Modern capitalism cannot survive without captive labor, who necessarily suffer, in order to keep costs as low as possible. This—modern corporatist capitalism—is not “right livelihood” in Buddhist terms, but people today are stuck within a system that is oblivious to the needs of the majority of people, spiritual or economic, or even sustainable in any sense. Capital can move on, after destroying an area, impoverishing the captive populations. Thus, we face the continuing crisis of global ecocide for ‘profit’.
The only “invisible hand” evident in today’s economy is one that pops out to sweep whatever is on the table into some private pocket. Quant-trading firms are only the most recent and efficient example of this, in the financial trading markets.
Compassion towards all sentient beings is more than an “ideal” in Buddhism, it is the path to accomplishing everything else, including our survival as a species.
Update to the OP’s update:
I’d like to correct some of your assertions. I am doing this because you are making assumptions about the Buddha and Buddhism as if they operated under the same understanding as economists, which is not the case.
The Buddha does not ”empathize with” anything. The Buddha manifests what is known as “Great Responsiveness” (Mahakaruna), which is often translated as “great compassion.” It is different though, than the compassion that unrealized humans can manifest, as it is not a feeling of compassion towards the suffering of others.
It is, instead, a mode of being in which all actions are directed spontaneously towards the benefit of all beings in each context (moment). This does not exclude the one manifesting the responsiveness, but includes all, thus it is not altruism—in its normal sense—either. (By that I mean that in Buddhism, “selfless” (Anatta) means something totally different than “selfless” in economic theory.)
Thus, when the Buddha taught, for example, his answers were always slightly different, just as his questioners’ understanding was always slightly different, and just as yours and mine are slightly different. This difference in teachings was not something planned, they arose spontaneously. I want to emphasize that because it is so different from the world we believe we live in, unless you happen to be an engineer who has to deal with the stochastic nature of electronic components on a micro-scale, where the spontaneity is something one has to always design for.
So, think of Mahakaruna as the great Market in the sky, making sure everyone involved goes home comfortable with what transpired, only really, and not just in some abstract, in the best-of-all-worlds, kind of academic hypothesis. Because, while Smith could assert “that following one's egoistic self-interest leads to the optimal (economic) results” he could never prove such a thing, and our experience to date is strongly indicative that no such thing is true.
I’d also like to point out that Smith’s “recipe” is only simple if you exclude the monetary system, banking system, communications technology, shipping capabilities and the infrastructure all that needs, storage facilities, corporate transnational legal structures, blah, blah.
In short, Smith’s “recipe” is only simple because all of the hard work has already been done. Unfortunately, it all got sold at a steep discount by corrupt politicians to greedy—as opposed to just ”self-interested”—people, who have undermined the proposed elegance and positive benefits of such a system, in order to aggrandize their own wealth, no matter how destructive (i.e. costs foisted off on the public) their activities are.
It may be true that communism and socialism (not the same things in theory, just in historical practice) have failed, but corporate capitalism is in the end months of ecocidal destruction of the world.
And whatever corporate capitalism actually is, it is lightyears away from anything Smith ever envisioned—but more to your question, it is anathema to what the Buddha taught.