Well since you asked...
The short answer is that the United States as a nation is chiefly founded more on English or German (bear with me here, yes Ostrichreich is not “Germany”) heritage, and not of Romance heritage.
The House of Savoy, as more of an Italian set of rulers, has the weakest of these claims that you list. It is worth pointing out that Jacobite succession did pass through them in the 19th century, but that claim now resides under the House of Wittelsbach, who themselves as good Bavarian Catholics are probably a better American choice as opposed to the more Italian Savoy.
That said, Bourbons have a few decent claims to a Catholic American throne. If it were not for the French (and Spanish who also have Bourbons and Dutch), the USA would likely not have had the resources and power to defeat the British in the American Revolution. The United States through territorial expansion, whether actually done or imagined, often went through French/Spanish colonial possessions. The USA had a provision in the Articles of Confederation for Canada to freely join the compact, but in reality they meant Quebec as a branch to the French-Canadians now under British rule who might want to get out. The USA also probably should have annexed the entirety of Mexico under the treaty of Guadalupe Hidalgo, but there were fears among Northern WASPs that such an annexation would break the balance of the USA as a land for White Anglo-Saxon Protestants, and also give too much territory south of the Missouri Compromise line for slave states to expand their holdings (even if much of Northern Mexico is not really suitable for plantation-style chattel slavery and Mexico had banned slavery). But those territories won in the Mexican Cession, and in the Louisiana and Florida acquisitions, were very much in line with historical Bourbon lands, and a displaced Bourbon could rule over a monarchy in the USA as a nod to their help in the American Revolution.
Speaking of Mexico, it is not hard to see how Hapsburgs fit into a North American context there. They are probably the most prominent Catholic monarchs of the period who ruled over a multiethnic and multicultural land, which would be a benefit to governing the USA. It is also worth noting that German has been put up before as a national language, and the only American President to not speak English as a first language spoke a language formerly ruled by them (Martin Van Buren’s Dutch). There were many waves of German-speaking migrations to the USA as well. It is not the dominant British and Irish cultural heritage, but it is an intriguing one in the American context. If you are choosing a royal house based purely off of commitment to the Catholic faith against the scourges of Protestantism, you would not do much better.
Perhaps if Mary I had lived longer, or had a child, then the Stuarts would be mostly irrelevant. England was reverting the Protestant reforms undertaken by Henry VIII under her reign, and they were actually making a lot of progress at restoring the Catholic faith to the first nation founded with the blessing of a Pope. The Province of Maryland was founded during some efforts at Catholic restoration in Britain about 80 years later as a haven for English Catholics, and it might be entirely possible that the English would have restored Catholicism as a major faith prior to the Glorious Revolution. Of course, Maryland was settled by other groups which drowned out its Catholicism a bit, and in the years following the downfall of the Stuarts Anti-Catholic sentiments became very baked into the English-speaking world. Yes, for example J.R.R. Tolkien was bitterly disappointed that his friend C.S. Lewis became a Christian in the Church of England as opposed to his Roman Catholic faith, but for the most part Catholics were quite alienated in the British Isles (also no doubt harmed by the British Monarch being the Head of the Church of England and expressly forbidden from being Catholic, and the nonconformism that such a status against that). My own personal sympathies are that this is the most likely path for an American Catholic Monarchy, although perhaps by that time the foundation of the USA as a land of religious freedom (but not always tolerance, and not always freedom in specific colonies) the ship would be a bit far gone unless some major changes occurred; indeed only a pitiful few signers and representatives to important early American documents were Catholic, and they were almost all from Maryland.
The USA is really the first, and perhaps greatest, experiment of what a Western nation looks like without having a Catholic heritage or infrastructure. It may have assimilated many formerly Catholic lands in its territorial expansion, but Catholics in general feel a sense that they do not belong in the USA; although this has perhaps lessened after Vatican II as changes to liturgical and doctrinal practice have led Catholics to look more like Protestants in the USA (perhaps aided by other cultural changes such as the racist heritage of abortion becoming an issue that Protestants starting caring about in the aftermath of Roe v Wade, but this is a different story). But as the largest single religious entity in the US (sure if you add all the Protestants up they are larger, good luck getting them to agree), there certainly is something to say about such a possibility if Americans ever installed a proper Monarch.