I have heard it said (but have no source) that the obligation to wear tefillin covers the entire day, and that people used to actually wear their tefillin all day long. (Various passages that I have seen in the gemara, of people removing tefillin to go to the toilet and replacing them afterwards would support this). Now that we are no longer able to focus our minds on clean thoughts for such a length of time (or so the story goes), we only put the tefillin on once and in the morning. This is why a person who forgot to wear tefillin by shacharis, or who forgot to daven shacharis, should put on tefillin in the afternoon for mincha.
But if the mitzva of wearing tefillin goes for the entire day, why do we need to supplant it with a one-time obligation? Why don't we say that all day-time davening (shacharis and mincha) requires tefillin? Why don't we encourage the use of tefillin at other points of time as well - such as when saying birkas hammazon, for example, or learning/teaching Torah?