What if…captured stones were removed at the end of the next player’s turn? This would make the basic ko rule implicit, so there would be no need to remember the last move. You just wouldn’t get to play on your own dying stone:
This eliminates the unfairness of having to pick up captures while your clock is ticking, and it seems more polite and sanitary, since you never touch your opponent’s stones.
An interesting consequence would be that you wouldn’t get to play a snapback immediately:
In the position above, White would need to play a sente move elsewhere before returning to kill the three black stones. If there is no large enough threat, Black would live. In fact, many normally dead groups might actually be alive in the absence of big ko threats.