Your calculations are not correct at all. For a proper comparison of chlorine costs, see this post
. Prices vary around the country (see this thread
for example), but generally Trichlor is the least expensive, but not that much less than some bleach (on sale) or chlorinating liquid (depending on pool store) and then Cal-Hypo is somewhat similar, Dichlor is then more expensive, and Lithium Hypochlorite the most expensive by far.
1 gallon of 6% bleach (that's Clorox Regular that says "6% Sodium Hypochlorite" and also says "5.7% Available Chlorine" because it's registered with the EPA as a sanitizer and may be used in pools) is equivalent in the amount of Free Chlorine as 12.8 ounces weight of Cal-Hypo 65%, 9.0 ounces weight of Trichlor (a little more than one 3" puck which is typically 8 ounces), or 14.9 ounces weight of Dichlor (dihydrate, the most common kind).
1 gallon of 6% bleach in 10,000 gallons raises the FC by 6.17 ppm (I won't get into why it's not exactly 6 or 5.7, but a rough approximation is just to use 6). It takes way more than a couple of teaspoons of Cal-Hypo 65% or Dichlor to raise the FC that much in 10,000 gallons -- it takes almost a pound, as indicated above. It's around 1.5 cups of Cal-Hypo -- that's 12 fluid ounces or 24 tablespoons or 72 teaspoons. Perhaps you were thinking about a spa?
Maybe you are talking about bleach that is extraordinarily weak, but even no-name regular bleach is around 3% typically. No-name "Ultra" bleach is often 6%. Or perhaps you were comparing by weight in which case you are right that when you pay for bleach or chlorinating liquid you are paying for mostly water, BUT the price per pound is very low.
Also, with Trichlor, for every 1 ppm FC you add you also add 0.6 ppm Cyanuric Acid (CYA). With Dichlor, for every 1 ppm FC you add you also add 0.9 ppm CYA. With Cal-Hypo, for every 1 ppm FC you add you also add 0.7 ppm Calcium Hardness (CH). With bleach or chlorinating liquid (or lithium hypochlorite) you do not get any additional CYA nor CH. The main disadvantage with bleach and chlorinating liquid is that it is a very bulky form of chlorine (due to the water) so is inconvenient from a "carrying from the store" point of view and it isn't slow-dissolving so you have to add it every day or two unless you have an opaque-to-UV pool cover in which case you can usually add it twice a week. You can get The Liquidator
for automatic dosing of bleach or chlorinating liquid if more convenience is desired (or you can get an SWG that generates chlorine using extra salt initially added to the water).