Can I drive 16 x 7-segment (or 8 with DP) displays, with no shift register?

That is of course the principle. If you are going to multiplex, you want to devote as much of the time as possible to each "row" that it turned on, so if your array is 16 by 8, you want to power each set of 16 for one eighth of the time, rather than each set of 8 for one-sixteenth of the time.