Historically these were the first implementations of DDE solvers until users need fancy things like discontinuity propagation.
If the equations aren’t efficiently integrated by low order scheme, it can be useful to use a nice ODE integrator like Stan’s to do the time stepping, passing the matrix of states over time as a parameter, and reference the state history from the ode func.
The main difficulty in Stan is that interpolation of history isn’t going to work (well).