This seems to make impossible a fairly classic fantasy trope (I'm thinking especially of REH's Conan): the assassin strikes but the hero sense the strike coming, turns and cuts down the assassin.
Mechanically, that looks like: the action 'I strike" is declared for the assassin; then initiative is rolled, imposing whatever penalty for surprise is appropriate; despite the penalty, Conan's player wins the initiative roll and Conan whirls and cuts down the assassin.
I'll admit that
@Dausuul's approach has a different issue: that the action can be declared for the assassin that triggers the initiative roll, but they don't follow through when their turn comes around (yay stop motion resolution!).
These problems with initiative systems and turn-by-turn resolution are one of the reasons I regard them as metagame frameworks rather than as corresponding to something in the fiction.