Jon, we used to have Finish DW detergent available over here, but no more. It was an old brand from the 1950s. Most of the powder DW detergents have had the chlorine removed although chlorine bleach is still available in most of the gels. Without the bleach, plastic tanks and plastic articles accumulate stains which can be removed by buying the new product sold with the rinse fluids and it will bleach the stains out of plastic articles.
I really dislike these new strongly scented detergents that leave an aroma in my plastic sports' bottles. The tea and water I put in them got a weird secondary flavor. I had to do some heavy bleaching to get that out of the plastic so now I make sure to buy baking soda scent or another non-flavored, detergent.
I don't know if one of the tablets would fit in an old D&M sideways pop-out detergent dispenser, but it might be interesting to try. Some of you might remember that as soon as the timer advanced into wash fill, the dispenser would fly open and scatter undissolved detergent on the wet items in the load, making distinctive marks on aluminum and causing slight damage to some flatware in the basket. I wonder if the cup would throw the tablet so hard that it could be heard hitting the inside of the tank or maybe an item in the lower rack or if the tablet would have to be wedged into the cup so tightly that it would not fly out.