I imagine you'd see a return to the TTL-based computers of the 1960s and 1970s built of discrete logic chips (TTL at the time).
If you still have access to modern manufacturing at the PCB and simple component level, something in the vein of retro-hobby projects like the MOnSter 6502 and the Gigatron, which reimplement a CPU using only TTL logic chips.
(ie. chip designs from before VLSI that are just the 1960s-state-of-the-art way to pack 3 or 4 transistors into a smaller, easier-to-wire package.)
The Gigatron kit does use a RAM chip and a ROM chip, but those can be built using transistors and diodes. (and capacitors if you want dynamic RAM) They're just significantly more bulky and, since it's a hobby kit focused on making a CPU without a microprocessor, it'd be counter-productive for the Gigatron to do that.
(See Visualizing ROMs 1: Diode Matrix ROM (Hackaday) for more on building ROM from scratch.)
...and I do hope you do have access to things like surface-mount transistors and pick-and-place machines or it's guaranteed to be cost-prohibitive as a consumer product. Even the Apple 1 used the kinds of complex ICs you're trying to avoid and it was pretty pricey after inflation despite how minimal it was. In this day and age, we take for granted how high the base cost of stored-program computing is.