I am merely here to relay the textual account on the basis of Chinese sources. It is what it is. There are certain clothing “orthodoxy markers” in Indian culture that do not translate perfectly to other countries’ ideas of what clothing is (some of these concepts were also found in other ancient societies). These include:
-unstructured cut
-manner of wearing robe like a brahman’s sacred thread, exposing the right shoulder.
-no bra or kancuka (these are believed even today in orthodox Hinduism to accentuate breasts and therefore be immodest)
Additionally, my understanding is that it is required for nuns to cover the places for which consensual touching would be a parajika, i.e. from the collarbone/shoulder (Dharmaguptaka & Mahasanghika=armpit) to the knee. The Sarvastivada vinaya clarifies that the “places normally covered by clothing” are what is meant here. Thus, the wide angsa has both modesty and cultural propiety elements.
The definition of an immodest women in the Jatakas and Jain sources is someone who deliberately arranges her clothing to show upakacchika, i.e. below the armpit, such as the breasts. Hence the samkacchika- the prefix sam has a sense of covering or complete closure here. But if we look at the cultures which inherit the older Indian women’s clothing styles (mostly tribal), they do in fact have a higher tolerance for open sided robes (“pata”) in general. As a garment worn close to the body, the samkacchika, even with the side slits, is already significantly more covering than a robe worn fully open sided without a sankacchika. It has therefore been regarded as a symbol of modesty in India.
Yijing had commented on the short sewn sankacchika he saw outside of India that it should be made longer to be Indian style. I didn’t get a sense that he saw the short one as offensive, just non-Indian. Vistors to India today might notice that butt coverage is a strong cultural norm still visible in garments like the kurta (salwar kameez top).
In addition to not being Indian, the short sewn one deviates from the textual tradition in terms of measurements. Some vinayas include length measurements for sankacchika, off the top of my head, the Mahasanghika gives 2 x 4 [hatthas] (approx 80-90cm x 160-180cm) max. Yijing also gives a length of 4-5 hatthas.
The link I had given for Taobao shows a sankacchika with vinaya based measurements.
The left hand flap issue can be partially solved by a belt over the top of the sankacchika, which seems to have been the norm in many places where similar garments were worn, such as with the chiton in ancient greece. But ultimately, the sankacchika is ancient inner wear…it has its own quirks. 
