From an engine and state-space perspective, a "Dark Souls mode" creates a massive challenge.

Explosive Search Tree: Because moves overlap in time, evaluating positions via traditional brute-force depth/breadth search becomes nearly impossible. The state space expands exponentially (or infinitely, without cooldowns).

Strategy over Calculation: Because an AI or player can't brute-force every micro-timeline, win conditions rely far more on high-level positional control and timing anticipation rather than raw calculation.

Endgame Dynamics: Cooldown management would dominate the endgame. It could either make drawing much easier or completely alter fundamental checkmate patterns (like King + Rook vs. King).

Great concept to think through!