When you export video, if you are having BI add the time, you are re-encoding the video, and that is inefficient and takes more storage than not re-encoding and depending on the size of the export, could take a long time.
The biggest reason not to use the BI overlay though is that the attorney and law enforcement members here have said that having BI add the overlay constitutes a manipulation/modification/altering of the video after the fact and in a lawsuit, a good defense lawyer would claim the video has been altered to try to get it dismissed in court.
The reason being you could overlay any time you want on it after the fact.
Sure a camera could have the wrong date and time too, but that cannot be altered after the fact.
It would suck to have great video of a crime and have it tossed on a technicality.