All of the solvents mentioned -- ethyl alcohol (aka "alcohol"), glycerin, table sugar, and propylene glycol, as well as other sugars, glycols, and alcohols -- are all related in that they all have one or more hydroxyl (OH) groups in their structure.
Soap molecules are highly soluble in any solvent or mixture of solvents that contains OH groups. When soap is dissolved in a solvent like these, the usual crystalline structure of the soap cannot form. Little or no crystalline structure => transparency or translucency.
Even castor oil is helpful when making transparent soaps. Castor is often used at a higher % in transparent soaps because it too has those helpful hydroxyl groups in its structure. Even in castor oil, those OH groups disrupt the formation of soap crystals, so castor oil also builds in more transparency. (And those OH groups are why a small addition of castor to a soap recipe will boost the lather in soaps with a blend of fats, even though a pure castor-oil soap doesn't lather much at all.)
One of the problems with transparent soap, as someone mentioned above, is that adding solvents to the soap makes the soap softer and more pliable. The solvents can also evaporate (especially the ethyl alcohol) which causes more shrinkage than you'd expect from a regular bar of soap. Table sugar can create a white haze on the surface of the soap called "efflorescence" as the water in the soap evaporates and the sugar crystallizes.
The point of using several solvents to make transparent soap is safety, cost, and long term good appearance. You could use just alcohol, as the original Pears soap was made, but you would need to consider the safety aspect of working with an expensive, highly flammable solvent. Many modern recipes for transparent soap avoid ethyl alcohol entirely, and I can truly appreciate why. High proof alcohol is not sold at all in some countries and US states. It's expensive where it is legal to be sold (like here in Iowa), and it's so very flammable. You could use just glycerin, a moderate cost, safe solvent, but the resulting soap is likely to be soft, pliable, and weepy. You could use just inexpensive table sugar, but the soap would eventually get efflorescence on the surface, greater shrinkage with time, and the soap can also weep in high humidity. Propylene glycol and sorbitol are modern solvents that attempt to avoid some of the problems of the older solvents (ethyl alcohol, glycern, and table sugar). The use of several solvents is a balancing act to get the best outcome.
Another problem with transparent soaps is the limitations on the types of recipes that are best suited to transparency. Theoretically you can use any soap recipe to make transparent soap, but some fats will result in the soap being only translucent vs. near transparent. The recipes best suited to high transparency don't necessarily make the best soap for the skin. A transparent soap will also not last as long because it's soft and will wear away faster, since it contains a high % of solvents and a lower % of actual soap. It's also not as long lived because it doesn't have the tough crystalline structure of a "regular" soap to reduce its solubility.
Not trying to argue anyone out of making transparent soap -- just pointing out the pros and cons and giving a little chemistry background. I'd like to make transparent soap one of these days myself, so it's been something I've been studying up on.
