Instead of that, Waze stores the recent drives you navigated to.
Also you can save them as Favourites
Why should we get searches we didn´t navigated to?

The hint is that Waze is not only a GPS which gives you a route to a place. It's a social GPS where you and other users record the route conditions on real time, so it can suggest you a better route to a point you navigate daily if there's a traffic jam...

So I take it Waze doesn't do that.

That one searched for a place signifies a potential interest, and increased likelihood of repeated search and navigation. Hence Google Maps saves it, and appropriately so.

One can pose an argument as to why Waze shows place we already navigated to? I've already completed my journey, so why bother? It can go both ways.

Agreed. But I'm not sure what that's got to do with saving and displaying search history. It's all about storing a snippet of text that I previously searched for, so that I don't have to type in again. Efficient routing and all that comes much later.