While it's true we typically think of textile armors being most susceptible to penetrative thrusts, multiple instances of convergent evolution in weapon design across nations and centuries developed cutting weapons with extremely fine edges to deal with layered textiles.

From type 1a falchions to Indian tulwars, Turkish Pala, and Persian shamshir, fine-edged cutting weapons have proven to be effective against layered textiles. The ability of a fine, hard edge to cut fibres is part of the reason broadhead-style arrows are more effective than needlepoint styles against gambesons, and the same physical principles apply to sword design.

For the large part, indian swords have hilts which restrict the hand into a "hammer grip", with the wrist locked at a 90 degrees angle to the sword. This is true of tulwar, khanda, sossun pattah, golia, tegha and a few more designs.

The curve of the blade on tulwars, tegha and golia, and fine edge geometry, means that the only efficient, effective way to use these swords, with their hammer fisted grips, is to perform a "drawing cut". "Swordsmen of the British Empire" contains several accounts of British officers encountering tulwars and noting the draw cutting style used, and the deep wounds produced.

A drawing cut refers to the act of "drawing" or "pulling" the edge of the blade along the length of the target during the cut, rather than "chopping" at the target.

In a geometric and physical sense, this has a compound effect. A curved blade, drawn at an angle across a target, has a shallower edge angle, and is thus better at cutting. And secondly, the draw cut means the edge is in contact with the target for longer, increasing the probability of cutting each individual fibre of the fabric.

The ultimate combination of these factors is that draw cuts from fine-edged, curved blades is that they can quite reliably cut through layered silk textiles, and cheaper textiles too.

This design optimisation was not unique to India, with other regions also making cutting blades with similar design features - like the Pala in Ottoman Turkey, that used a T shaped spine (like a tegha) which allows for a very thin, fine edge. Likewise, they were used for draw cutting, and perhaps more extremely than even Indian swords, had such thin foibles -as thin as 1.5mm - (in the last third of the blade) that they were quite incapable of thrusting. (Primary data based on antiques).

It's also worth noting that thrusting weapons did coexist in India with cutting weapons - cavalry lances, often of a narrow and highly pointed design, were popular. Firearms were also extensively adopted and used, as well as other projectile weapons. Maille in particular was countered with pole weapons and lances, as well as by projectile weapons. Golia, or shamshir - bladed tulwar, also had very accute points and could conceivably pry apart links in Maille.

We also see the adoption of thrusting blades on firangi - literally "foreign" bladed Indian swords, which used tulwar and khanda hilts, and European made (or inspired) designs, including literal sidesword and rapier blades. This may have filled a niche for thrust-centric techniques.

On the topic of european blades, Benjamin Sydenham, an aide-de-camp to Richard Wellesley, stated that:

"it is perfectly certain that that these stuff and quilted jackets were frequently found to resist the sabres of even European Cavalry" - Moienuddin, Mohammed, Sunset at Srirangapatam. After the Death of Tipu Sultan, Hyderabad, 2000, p. 92

So it is clear that European blade designs, which were not optimised to the draw cut, could not cut padded Indian armor. I would also surmise that only a well made draw-cutting blade with a good cut, well executed, could cut good Indian padded armor.

A further potential explanation for the prioritisation of cutting designs - at least in the heyday of crucible steel - is that the vast majority of crucible steel blades made of Indian ores and processes cannot be tempered to a spring without leading to brittleness due to phosphorus presence in the steel, and the high carbon content inherent to crucible steel, which combine to make less durable blades when quenched and tempered in the typical way. (Verhoeven et al, 1998, key role of impurities in ancient damascus steel)

A cutting sword made of crucible steel distributes force along the strongest plane of the sword - there is much more rigidity along the edge, than along the flats - thus it is a better use of an otherwise unpredictable material like crucible steel. Thrusting weapons necessarily need to flex a certain level when they encounter bone, and they flex upon the weakest plane - the flats of the blade. With a pearlite tempered crucible steel blade, the sword will remain bent after exceeding its elastic limits, but will not break. (based on the aforementioned research by Verhoeven et al, and personal handling of antique crucible steel from indopersia.)

The development of arms and armor is complicated, and the impact of material, technology, fighting systems, fashion, tradition, and the arms and armor of neighbouring regions all play a part in determining how weapons and protective equipment are designed.