Tvtropes call that a Last Episode Theme Reprise, and mentions that it is used in video games as well:
Since it's standard practice to make a Theme Song as awesome as
possible, said theme likes to find its way into a privileged position
in the final battle. At The Climax of the series, when things are at
their most epic, the theme gets played over the show itself. Typically
we'll get to hear the verses not played in the opening, and sometimes
the whole song is strung together for once.
The opening or closing theme can be used. Often this serves as an
ultimate Theme Music Power-Up. Often it serves in this capacity for
the show itself. The creators seem to be claiming their own Crowning
Moment of Awesome with this music.
This is also common in Video Games, the most common being a reprisal
or orchestral version of the main theme over the final dungeon or
ending sequences.
I would say that it is at least not uncommon, since the page has an extensive list of titles that use this trope, to name a few:
- Neon Genesis Evangelion
- Dragonball GT
- FMA
- Eureka Seven
- Witchblade
and many others. As for Is there a reason for it (as opposed to just playing a new epic piece), usually there isn't. If it is significant, however, it rather seems to be the Title Theme Drop trope;