All languages express aspect in a more or less prominent way whether in the verb form or the overall context it doesn't matter. Since people are familiar with the "reality" of aspect terminology is of a secondary importance. Grammar is a toolbox to help us learn a language. If one of the tools is not needed it should stay in the box.
Anyway, no matter how clear the distinction is and no matter what terminology we use it all comes down to usage and sometimes usage defies "categories".
Ireney, Well said! You have expressed my thoughts about this 'aspect' business