Why the 7400 chips? :) The MC14000 / CD4000 family was available back then. Most designs that didn't use CPUs wouldn't multiplex since the displays were driven by parallel outputs from counters typically, or from parallel latches. The multiplexing for parallel latches was done on the bus side, naturally - each latch was an addressable write port. The decade counters would be, well, used for counting, so no multiplexing involved - they were just chained into a long chain of decade counters, as many as there were digits. Then either a counter would have a 7-segment decoder and a parallel latch built in, or there'd be a separate latch/decoder.
I'm using shift-registers to move data from the counting circuit to the 7-segment decoding circuit.
Why? The decade counters can drive the digits directly. You're in the 1970s. LED displays are dim. Nowhere near as bright as those you can get today - at least an order of magnitude worse in terms of energy conversion efficiency. They also didn't take much heat before degrading, and were generally fragile compared to modern LEDs.
In the 1970s, you'd most likely not want to multiplex LEDs, since they'd be too dim. Especially in applications where you'd want a range of usable brightness, e.g. a brightness adjustment for the display, like in avionics etc., no multiplexing of the display was involved. The bus linking the digital signal source to the display could be multiplexed, but the displays would be driven statically at 100% duty cycle. Optional brightness adjustment could then either reduce this duty cycle, or decrease the effective voltage seen by the segments. This would be typically done not by lowering the supply to the driver chips, but by raising the common cathode voltage, or lowering the common anode voltage.