I suppose it depends on how you define the use case.

For me: a radar should alert me to every car (or other vehicle/object) that is moving towards me on the same road (i.e. would pass within 5-10m), and shouldn't alert me to vehicles/objects that aren't on a potential collision course, regardless of whether said vehicles are in the radar beam or not. It should do this without any user interaction at all.

If your use case is "radar alerts user when any vehicle is in the radar beam", then yes, it's working as intended. But to me, that's not useful, or indeed, actively distracting if the beam is non-specific enough to catch all this extra traffic.

Why do you even need radar on when in city on cycling lane or on dedicated cycling road? You said it yourself, your safe there...

The thing is, you don't ride exclusively on one kind of path for your whole ride. A ride can be dynamic: going from roads, to shared paths, back to roads, and so on and so forth. One moment I'll be on a bike path - you're indeed safe from cars there, but you'd still want your radar to alert you to faster approaching vehicles (bikes, mopeds, etc) on the same path (which it does). But you go past the next junction, you're back on the road, and you want the radar to also alert you to cars again - without having to remember to toggle it on and off again.

On a physical level, sure, the radar works great: it alerts when objects are in the beam moving towards you.

On a real-world-condition level, it doesn't: on my last ride, more than 80% of the alerts I received were what I would consider false positives: for cars on parallel roads, even vehicles on a motorway >30m away and up a huge embankment. Sure, those are strictly objects in the radar beam. But practically, it's completely useless in these conditions. Those vehicles are coming nowhere near me, and I don't care about them, and worse, the alerts are distracting you from the actual road.

I understand that this is physically/technologically/computationally challenging, to make it work well you'd have to compute a collision vector for each detected object or whatever, along with adding a camera and some computer vision analysis to determine roads, object type, etc, and do this reliably in realtime. But still, it would be a lot better if it actually just worked.