I’m not sure it is about (not) triggering unwholesomeness. Otherwise they would not sit with a shoulder uncovered to give a dhamma talk. Uncovering the should is a sign of respect. One I am guessing historically this is due to showing you have no weapons on your right hand side (my speculation).
I also speculate that the covering of both shoulders was to protect from wind, sun, bugs and other creepies. As reflected on in the reflection on the 4 requisites. The modesty aspect is covered just by wearing the robe either way.
This from the BMC, regarding the sekhiya rule on wearing the robe:
Sekhiya 3-4 - I will go [sit] well-covered in inhabited areas: a training to be observed.
The Vibhaṅga does not define inhabited areas in this or any of the following rules. The term thus probably has the same meaning as under Pd 1: in the homes of lay people, or along the streets and alleys of villages, cities, or towns. This does not include, however, monasteries located in inhabited areas, for the incoming bhikkhu’s protocols (Cv.VIII.1.2) show that when the Canon was composed, bhikkhus were not required to wear their upper robes in the monastery. At present, though, many monasteries located in inhabited areas require that bhikkhus living with them observe many of these rules when outside of their personal quarters but still within monastery grounds.
Well-covered, according to the Commentary, means not exposing one’s chest or knees. One should have the upper edge of the upper robe around the neck, and the lower edge covering the wrists. The lower edge of the lower robe, as stated above, should cover the knees. When seated, only one’s head, hands, and legs from the calves on down should show.
Sekhiya 4 here has an added non-offense clause: There is no offense if one sits not “well-covered” within one’s residence (§). According to the Vinaya-mukha, this means within one’s room when staying overnight in a lay person’s home; when outside of one’s room, though, one should follow the rule.