This, of all the choices given me in the responses, is the best one.
As a confessor, when I impose a penance, the penitent is obliged to do the penance and, barring extraordinary circumstance, it should be completed before approaching the sacrament again. One should not, in other words, be accumulating uncompleted penances or seeing them as suggestions that one may do or not do – one is to complete the penance. So, yes, there was a purpose to saying “I completed my penance.” As it is, the rite currently presumes that the penance was completed in the absence of a statement to the contrary. As I have said elsewhere, there is no reason cannot tell me that they did their penance. It removes all doubt.
An uncompleted penance does not invalidate an absolution. Nor does it preclude approaching the sacrament again. But, one way or another, it should be addressed in that subsequent confession as either “I have not completed my previous penance because it involves a pilgrimage to the diocesan shrine, which I plan to make next week” or “I have found the penance impossible, Father, and need help”, etc.
Sadly, it can happen that confessors will impart penances that are not completed because they have no defined terminus or they are constructed in such a way as to make their completion hard to achieve or they are simply too vague for the penitent to know if they have achieved them. In such cases, it is necessary for a confessor to use his power to commute penances so that the matter can be definitively resolved.
A penitent is perfectly free to ask for a different penance from the confessor at the moment he proposes it. Some penitents do not seem to understand this. Were I, for example, to propose a day of abstinence as the penance I intended to impose, the penitent is perfectly free to say: “Father, I have a medical condition that precludes that…would you make the penance a prayer…such as Stations of the Cross here in the church?”
Finally, as a confessor, I do have discretion in imposing penances. There are indeed times when I will make the decision not to impose a penance at all. It does not affect the validity of the absolution.