Hi..
Just briefly.. There have always been some loop holes in the Mamluk origin theory. One of those is that the Mamluk cards did not have faces on the courts, while the European cards and the Chinese cards do. Plus, the European face cards look like the Chinese face cards, and so that hints at a direct influence.
The second reason is that I have always been facinated by Diane O'Donovan's work on early card history. She is well informed about Islam, and has decided that it is more likely that the emblems of the European cards began in a Spanish/Sicilian culture heavily influenced by Islamic cartography, then traveled east rather than the other way around. I would have to reread her work to remember all her points.
And finally, I have a very speculative theory about the card origins that matches more closely with the occult attributions of the four suits relating to the four elements, and medieval Platonism.
There is a travel journal that describes a very amazing banquet held in the Mongolian Court where Buddhist, Muslims, Christians, Nestorians, etc. all gathered to prove the superiority of their religions so that the Mongol King could decide. As was traditional in that time, there was a lot of heavy drinking. Eventually, the debate degenerated into drunken diatribes on each the religions' parts, that is, until everyone passed out.
Ramon Llull was a great admirer of the Franciscans who had traveled to the Mongol court. He created dialogues along the line of the banquet where the Muslims, Jews, and Christians have to present their religions to the court of undecided. His goal was to convert the Muslims, Jews, and Tartars using a universal art.
Now, suppose that the Franciscan travelers had picked something up like a mandala from the Buddhist, or an ancient symbol from the Nestorians, and they brought this souvenir back to Provencal. They called it the universal art, and perhaps along with it came some card games (unreported). Using the commentaries of Calcidius on Plato's Timaeus they devised their own version of the universal art using the four elements of fire, air, water, and earth. Maybe it was a Chinese dot card game arranged into suits with the four elements ruled by the courts. Later, it might have become an actual card game when paper became more available and yet it still retained some of the mystique of its origin as the "universal" art.
Here is Calcidius commentary on how the World Soul of the Timaeus brought together the elements: (taken from Stephen Gersh Concord in Discourse)
Attributes/combinations
Fire Sharp (King, Queen, Knight)
Subtle of Sword
Mobile
Air blunt (King, Queen, Knight
subtle of Rods)
mobile
Water corpulent (King, Knight, Queen)
mobile of Cups
blunt
Earth blunt (Queen, King , Knight)
corpulent of coins
immobile
Fire shares with air the subtle and mobile; Air shares with water the blunt and mobile; Water shares with earth the corpulent and blunt. The elements are knit together into one tight whole by the World Soul.
This speculation would make Platonism organic to the card suits, rather than imposed at a later date. The romance quality of the courts could have as easily evolved in the culture of Provencal as in the Mamluk dynasty, since there are common elements to both.
Of course, I share this knowing that this is not a provable theory. It does provide ,though, a rational for a some themes in occult Tarot--such as that it is the universal art. And this theme (whether attached to cards or not) was also in the Renaissance in Cusa and Kircher who tried to find a common tradition in diverse rites working from the Lullian combinatory art.