That's backwards. Esters and AN's both have high solvency, which is necessary to break-up existing deposits. Esters are also highly polar, which means they fight for surface space, so they can make additives fighting for that same space less effective. AN's don't have that problem. Detergents and dispersants are both designed to PREVENT deposits by keeping deposit-forming materials in suspension and preventing them from agglomerating, which can enable them to get large and heavy enough to plate-out. They do not clean up existing deposits, because they have no inherent solvency.
This is why products like HPL EC and the old AutoRX are both ester-based formulas and not just a metric assload of calcium or magnesium detergent.
A dedicated solvent will of course also do the job, and much faster, but they present their own challenges in terms of handling and delivery.