I can think of three reasons.
First, there is a placebo effect. For the Westerner/outsider, eating with your fingers seems exotic. For (many, not all) South Asians, eating with your fingers brings back memories of family and comfort foods.
Second, your fingers are highly versatile and they are often the best implements for consuming these foods and blending together spices, condiments, and foodstuffs themselves. There is a reason why humans evolved fingers rather than forks.
Third, and how shall I put this? A lot of South Indian food is vegetarian and eating with your fingers adds flavors of…meat. The fleshy sort.
Eating a dosa with fork and knife is a very different experience, for Tamil food on the palm leaf all the more so.