Add a component called a Redstone Converter. It has one input, one output, and an internal programmable table with 16 entries that specifies for each input power level what the output power level will be on the next redstone tick. The table entries are programmable via a UI panel. It should be clear that such a simple device would impose very little burden on the redstone processing loop, certainly less than a hopper.
Nevertheless, this device is extremely powerful and has thousands of applications. For instance, you could use 7 of them with a shared input encoding a number as a power level to drive the output lamps of a 7-segment display. You could use 4 of them to convert an analog signal encoded as a power level to a digital encoding, or up to 16 of them to perform 1-of-N selection. And you can reverse either of those to do digital-to-analog conversion or 1-of-N encoding into an analog signal.
There are pure digital applications as well. By feeding the output back to the input, you could make a counter that counts from 0 to N<16 and then repeats...or stops. You could use that as a sequencer to drive another converter that outputs redstone pulses in an arbitrary but precise pattern. Timing problems could be fixed just by reprogramming converters instead of reconfiguring the circuit to insert repeaters.
I can imagine that after considering its possibilities, you might think such a component is overpowered. It's true that compared with a repeater or comparator, it's way more powerful and would need to be expensive. But consider the educational value it would have. A smart kid could invent things nobody has dared to imagine in Minecraft because they'd be too big and complicated. In the process, the kid would learn the fundamentals of Boolean logic and analog signal processing.