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Congestion-pricing deployments often use simple, mostly static tolls. Recent work shows that with known demand, the revenue loss from doing so is bounded in canonical traffic models, but these guarantees assume the planner knows demand. In practice, demand is estimated from traffic that the toll itself shapes. We study whether simple tolls retain their guarantees under learned demand in a two-period congestion model with linear demand response and several extensions. The objective loss of any plug-in tolling policy is an exact quadratic form in toll error (Lemma 1), yielding the following results. (i) With known demand, the two-period price of simplicity is tight at \( (1+\sqrt2)/(2\sqrt2)\approx0.854 \), attained at demand ratio \( 1+\sqrt2 \); with H periods no constant guarantee holds, since the worst-case ratio decays like \( 4/H_H \) (Theorems 1 and 2). (ii) Estimation error increases the dynamic plug-in's loss relative to its dynamic oracle by at least as much as it increases the static plug-in's loss relative to its static oracle. The dynamic plug-in outperforms the static plug-in exactly when the true toll differential exceeds the root-mean-square error of the estimated differential (Corollary 3); the loss ordering extends to periods coupled by cross-period substitution (Theorem 4). (iii) This simplicity advantage applies to unshrunk plug-in estimators: certainty equivalence is Bayes-optimal in the interior regime, so a Bayesian dynamic planner weakly dominates a Bayesian static planner (Theorem 5), and a one-parameter shrinkage family interpolates between them with closed-form risk (Theorem 6). (iv) The static-optimal toll is identifiable from aggregate flows under one fixed toll, while the dynamic-optimal toll is not identifiable under any interior toll sequence (Propositions 1-2). (v) Under random-walk demand, batched re-estimation has an interior optimal review period; a continuously updated Kalman filter strictly dominates every batched schedule even with revision costs, and a one-time estimate never recovers from a demand shift (Theorems 7 and 8). We verify closed forms with seeded CPU simulations and report discrepancies.