Why can't everything be run on AC?
In engineering, we try to solve a problem in the best way. Best is a mixture of cheap, fast, simple, reliable, etc. and the best choice may shift over time.

Circuits that work directly on AC power might be possble, but so far they are not as good as DC circuits, so for an overall system it is much better to make the AC into DC (at the cost of some extra circuitry) and use DC powered circuits, than to use AC powered circuits. For some very simple circuits like relays, heaters, mains-synchronous motors, lamps, etc. AC is often used directly.

One quite fundamental problem in AC power is that there are periodic moments where the voltage is zero. It is quite difficult to design a circuit that operates well at 0V. Remembering a state (1 or 0) through a period of zero power is also difficult.