Detergent is built to clean what is inside the drum. Dish soap is built to clean what is on the plates. Neither one is aimed at the machine, and no amount of either will shift what is stuck in a gasket fold or baked onto a spray arm.
That is not a flaw in your detergent. It is a different job, and it needs a product dosed for it.
In fairness to vinegar
Vinegar and baking soda are not nothing. Vinegar really does dissolve some mineral scale, and if that is your current routine you are ahead of most people.
Two honest problems with it. It works on the surface rather than on the biofilm underneath, which is what actually causes the smell, so the smell comes back. And vinegar degrades rubber over time, which makes the gasket the one part of the machine you least want to keep treating with it.
A tablet is dosed for exactly one cycle. It fizzes into a foam that climbs into the gasket folds, under the agitator post, around the spray arms and across the grind chamber, lifts what is stuck to them, dissolves the scale, and rinses out.
Five ingredients
Baking soda
Citric acid
Washing soda
Enzyme blend
Coconut and corn surfactants
No chlorine bleach. Septic safe, greywater safe, vegan, cruelty-free.