You CAN measure the acid dissociation constant of, e.g., HCl. Which implies that there is no such thing as 100% dissociated. Nevertheless, it is conventional to label certain acids as "strong acids", defined as those that are fully dissociated under standard conditions. The discrepancy is that certain acids are so nearly fully dissociated that we can consider them to be such for most practical purposes. If an acid is 100% dissociated, then by definition the equilibrium constant is undefined, so it cannot be calculated. It can be measured, but the closer the degree of dissociation is to 100%, the harder the value is to measure accurately. For example, the pKa of HCl has been reported in older literature as being anywhere from -0.9 to -6.1, a spread of over 5 orders of magnitude. Even if we take the higher value as the true value, this would mean that HCl is >99.95% dissociated, so 100% doesn't seem a bad approximation. There are cases where the small portion of association of strong acids is important, such as membrane penetration.
I think your explanation is fine, except that I would qualify them as being impractical to use since they are NEARLY completely dissociated.
Interestingly enough, you will still find many veteran chemists who refuse to believe that strong acids aren't actually 100% dissociated. Goes to show how some of the general chemistry simplifications we learn early on can be hard to shake.