Excellent observations Jens, and I am inclined to agree, I would be extremely nervous having my most important finger out there subject to such danger!
While the Europeans did of course fight differently (actually parrying with the sword itself, while Indian combat practice typically seems to have dictated the use of the buckler to parry), it may possibly be a structural feature of the blade taken from the European blades?
Possibly it was perceived that the thickened area at the root of the blade would give more strength to the blade in its seat, and as Katana has mentioned, my suggestion of the 'choil' concept in sharpening the blade.
I think that we have established that there was distinctly a difference in hand size by mention of this in a number of sources, so the idea of the 'finger wrap' has lost a great deal of its feasability in general. There would remain of course a certain selectability, where in key instances it would be quite possible that a warrior might have held the tulwar with finger wrapped to insure firm grip in attack to assure solid hit, and if little or no opposition was seen or expected (i.e.surprise attack on camp etc.). Such application would seem a matter of choice, not necessity.
Again, if sword to sword combat possibility existed, it seems that finger should stay 'inside' the guard!
Best regards,
Jim