4 in series with each of the digits?
The problem with that is as more segments come on more current is drawn therefore more voltage is dropped across the resistor. That means that the digit's brightness depends on the number of segments that are on. So you get a bright 1 and a dim 8. The resistors need to be in each segment so 8 it is. That is the attraction of having constant current drives.
I had seen some references to putting high currents into LEDs
Yes a lot of LEDs have a pulse current specification that is much higher than the continuous current rating. The on / off ratio is normally quoted and it is used to compensate, to some extent, for the dimming caused by the on / off ratio. However, even so the current has to be managed to be within that specification, and it does shorten the life. A firm I worked for had a 10% return rate on set top boxes with high current pulsed LEDs even though the current was within the specification. Contracts often mention a epidemic failure clause that kick in at about 3% so there was a lot of fuss about that. When making a million boxes 10% is a lot. There were 19 LEDs on the box and it only takes one to fail for the box to fail, that is be returned.
However, the major problem with high pulsed currents is from the driver rather than the LED. The potential for doing damage is a lot greater because chips are of a physically more delicate construction than LEDs.
but I assumed that a commercially sold board would have investigated the ramifications of this and found out that the design was OK.
Ah if only that were true. Thing is, even commercial designs are made by people, with all the variability that implies. You should have seen some of the things I had to correct from my 'professional' engineers when I was a manager.