There are a couple of points here worth making that actually reflect hot cocoa as much as they do in making chocolate ice cream bases and the like.
Chocolate consists of cocoa solids, cocoa butter, and fillers/sweeteners/preservatives/emulsifiers (sugar and milk solids, depending on the stated %). Natural processed chocolate has a lower pH than Dutch process which add alkalizing agent to the cocoa nibs.
Soluble in water are obviously the fillers and so are some of the cocoa solids (partially soluble, partially suspended in a water solution).
But cocoa butter is not soluble in water. It floats. Not good.
The easy choice is to use hot chocolate mix which is mostly cocoa solids, less than 1% cocoa fats and emulsifiers (usually Lecithin from Soy and Glycerol Monostreate).
In Ice cream we prefer glycerol monostreate (E471) as it produces a smoother texture. Egg yolks can also be used as an emulsifier for the cocoa butter but the flavor becomes more like chocolate mousse.
Points to consider:
1. The use of a "real" chocolate (couverture, compund or real) requires emulsification and/or stabilization.
2. Emulsification requires an emulsifier and heavy beating with a whisk (to create the boundary between the continuous and dispered phases).
3. Conversely, using a stabilizer like corn starch also helps by thickening the solution (using the milk's emulsifiers to prevent separation - but also corn fibre gum is fortunately ambiphilic and can thus emulsify somewhat on its own - see https://ialimentoslem1.files.wordpress.com/2014/05/hydrocolloids-as-emulsifiers-and-emulsion-stabilizers.pdf
). I think it works in much the same way as a bit of mustard helps stabilize mayonnaise (mustard has Lecithin).
4. I could not find a reference for how pH aids stability*, except in a pass by fashion stating that acidity helps stabilize oil-in-water emulsions while alkalinity stabilizes water-in-oil emulsions (and that it has to do with the polarity of the extra ions). In theory that means natural processed chocolate should make for more stable emulsions.
Ramon Morales in Ch states that low methoxyl pectin can also be used to stabilize thick drinking chocolate. He also recommends E471 as a stabilizer if it is to be frozen for storage. He states that separation is inevitable from thin drinking chocolate unless emulsifiers and stabilizers are added and recommends that bottles be shaken routinely to avoid FLAG from forming ("Flag" due to the separation: Milk and cocoa fats rise as a white layer to the top, while dark suspended particles sink to the bottom, while the middle is the lighter solution - appearing like a 3 layer "flag").
His starting recipe for thick chocolate is 900gr Milk, 100gr 35% cream, 300gr 64% chocolate (must be couverture with lecithin), 30gr corn starch and vanilla and 1gr salt. For thin chocolate his starting recipe is 1000gr milk, 300gr couverture (71% cocoa mass), 1gr salt.
*Acids are usually key in water based emulsions due to spoilage concerns (where water is the continuous phase, any waterborne can spread to the entire batch; conversely, when fat is the continuous phase - like in butter - waterborne pathogens get stuck in their own little droplet and cannot spread through the fat surrounding it).
Caution! Water, heat, pressure and electricity don't mix! I want an espresso.