I do not think any historian would assume that what is currently public is all there is - quite the contrary, and part of their work, I would suggest, is similar to the archaeologist's: uncovering materials that remain to be uncovered, and presenting them contextually.
It is this contextuality that new finds also, with time, transforms. Not that long ago, it was indeed even believed by some historians that playing cards arose from tarot, or that perhaps 'gypsies' (or other migrating group) brought tarot to Europe from easternly sources.
Due to the uncovering of various texts, documents, and cards, those who have delved in history have clarified some points. This does not mean that all that is to be known about early tarot is complete - far from it, as both you and I realise.
Historians, however, bring to our attention important relevant materials that continue to form the basis of our historical understanding. This does not negate any spiritual undertones, nor the manner in which the spiritual may be reflected in tarot's rich imagery, containing echoes of still former times.