In cell-free massive MIMO, centralized precoding is {theoretically known} to {remarkably} outperform its distributed counterparts, albeit {with} high implementation complexity. However, this letter highlights a practical limitation {often overlooked:} {widely used closed-form} centralized {precoders} are typically derived under a sum-power constraint, which often demands unrealistic power allocation that exceeds hardware capabilities. {When two simple heuristics (global power scaling and local normalization) are applied to enforce the per-AP instantaneous power constraint}, the centralized performance superiority disappears, making distributed precoding {a robust option}.