**Question:** Let $X$ be a noetherian integral scheme. Is there a dense open subscheme $U\subset X$ such that $U$ is Jacobson?

I am happy to allow $X$ to be excellent and then the question of course immediately reduces to $X$ excellent and regular. Equivalently, we could also ask whether every noetherian/excellent scheme admits a stratification into Jacobson schemes.

Note that if $X=\mathrm{Spec}(A)$ is affine, then the Jacobson radical may be $0$ even though $X$ is not Jacobson. An example is $X=\mathrm{Spec}(D[x])$ where $D$ is a DVR (there are many closed points of $X$ sitting in the generic fiber over $\mathrm{Spec}(D)$).

What if $X$ is essentially of finite type over a field?