We have had something "theoretically secure" for like 40 years now, current research is more about how to make those ideas usable in practice (and ideally state

We have had something "theoretically secure" for like 40 years now, current research is more about how to make those ideas usable in practice (and ideally stateless), so I don't share your pessimism here. Those ideas are also fundamentally based on symmetric algorithms, which are already well understood. I would expect the transition to be fairly easy honestly (once a standard has been decently established), except for systems that are very constrained in storage/bandwidth, since either the keys or the signatures are going to become quite a lot larger.