You can multiplex displays, however there is a limit to how low the duty cycle can get without adversely affecting the brightness. That limit depends on how good the displays are (brighter more efficient LEDs generally cost more) and the specs of the LEDs (max peak current) and how bright your display needs to be visually, so it varies with the application, but typically 1/4-1/8 is about as far as you want to go.
Minimum component count might be a goal in small-volume applications such as oddball instrumentation, but for high volume applications, it's usually cost that is minimized.
If you're a hobbyist, then something like the MAX7219 which will control 8 digits might be a choice, especially since there are probably Arduino or whatever libraries available so that the effort is minimized. Genuine ones are pretty expensive, far too expensive for many volume applications. I believe there are cloned ones out there. You can use one or more and select using the /CS lines.
The more usual approach in volume applications is to use the microcontroller as the display controller and add some inexpensive drivers. The consumption of microcontroller bandwidth is pretty small (maybe a couple percent for an 8-bit microcontroller) provided the timer interrupts can be serviced with small enough jitter to prevent visual flickering of the display (probably a +/- a handful of microseconds will suffice). The number of I/O can be handled by picking the microcontroller for that characteristic or by adding expanders or shift registers or demultiplexers (for digit selection). You could also use a small CPLD, which tend to excel in having lots of I/O vs. cost, but that requires device programming and writing the code in the first place.
Generally speaking, the optimum trade-offs will vary with each and every design.
multiplexing
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