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The problem from a design view is, that the game would have to implement fine grained timing of signals, how they pass through gates, how they are synchronized. That would be very intransparent for players too. As it is the game can resolve all modules in any order and the result should be the same.
There are other circuits with feedback loops that would settle in a stable state but don't work too well either AFAIR. Basically any circular dependencies don't seem to work, or at least not well. At least the player is alerted to the problem and the game doesn't simply hang in an infinite loop.
It's a limitation of the game, but eliminating it would make the game logic much more complex.
Also i can't get my head around why sometimes a module seems to take an "internal clocktick" to propagate a solution, and sometimes it doesn't.
Looping solitions seem to be a bit brittle.
For future viewers of the post the S&H component functions as a D-Latch as apposed to a D-FlipFlop, which wasnt immediately obvious to me given its description, but seems like the issue. Still suffers from legitimate steady-state solutions mentioned by gotan above.