I think that’s a great point and something that inadvertently fits well together with the UNINOVE model, although there it looks more like an unintentional sideffect than a feature. Observe the two smoothest (top) and two most jagged (bottom) trajectories of beta (proportional to the current infection rate) for some regularized model (left) and the original UNINOVE model (right). (Note the quite different y-scales).
One could reintroduce the original stochasticity into the regularized model by letting
beta ~ normal(overall trend,stochastic noise)
where the overall trend could be even more strongly regularized. This might help with fitting / modelling.