Frontier AI systems function as \emph{constitutional institutions}: each deployed model encodes an implicit ranking among safety, helpfulness, honesty, autonomy, and equity. We ask whether the supply of frontier constitutional types covers human demand. Combining a paraphrase-controlled audit of the as-shipped default constitutions of
23 frontier LLM archetypes with a pairwise-tradeoff study of
1,649 US participants on the same instrument, we report three facts. \emph{Demand is broad}: it spans all five values, with the largest constituency under one-third. \emph{Supply is narrow and drifting}: the
23-archetype hull occupies
∼2% of the demand hull under conservative noise-matched estimation (
0.10% at full audit precision), no archetype puts helpfulness or autonomy first (
37% of users are constitutionally homeless), and across six model families autonomy decreases in
5/6, equity increases in
5/6, and safety increases in
4/6, with monotone within-family version trends (order-permutation
p=0.013) and the autonomy decline concentrated in scenarios where safety is not at stake. The drift's importance is directional: \emph{away} from a value already undercovered, mechanically worsening the welfare floor for the least-served users. \emph{The fix is sparse}: a
2-vertex menu
{eHON,eAUT} beats the full
23-archetype frontier by
47% on mean regret (CI
[43%,52%]); three vertex additions cut mean/worst-group regret by up to
81%/
64%. We formalize these findings as a budgeted-pluralism trilemma, show the binding regime is empirically realized, and verify the conclusions are robust to distance-based welfare and to degraded routing. The instrument and audit harness are described in full in the appendices.