  We show that the space of traces of the free group $F_d$ on $2\leq d \leq
\infty $ generators is a Poulsen simplex, i.e., every trace is a pointwise
limit of extreme traces. This fails for many virtually free groups. The same
result holds for free products of the form $C(X_1)*C(X_2)$ where $X_1$ and
$X_2$ are compact metrizable spaces without isolated points. Using a similar
strategy, we show that the space of traces of the free product of matrix
algebras $M_n(\mathbb{C}) * M_n(\mathbb{C})$ is a Poulsen simplex as well,
answering a question of Musat and R\ordam for $n \geq 4$. Similar results are
shown for certain faces of the simplices above, such as the face of
finite-dimensional traces or amenable traces.
