Just come across this site as I was taken to task for NOT including stops in eg and wanted to definitively know what's the formal line on this.
[Waaah! EeeeK! Your website wouldn't allow me to write eg. It wanted e.g. !! A subtle ploy to MAKE me do it?]
I have not used stops in dates and abbreviations in years. I agree that it looks cleaner without; the time for old-fashioned flowery style has gone. Even official documents are no longer in this style so we do we need to be? Language, spoken and written evolves. As for saving time: does it? I don't think in this day of fast keyboards that it does but it just looks simpler – and that does it for me.