You expect people to start running at 5-6km/h which is about a fast walking pace? That seems unduly slow?
Heh, don't get old or be born with the wrong genes. I have to start at no more than about 2min at a time being middle aged now. Some of us are born weaker and more fragile. Aging only makes this worse.
Strength training can help, though I've accumulated enough stubborn injuries now that I'm just thankful I can do anything.
I mean physically, what am I supposed to do to run at 5-6km/h? Should I exaggerate and slow down my run stance? Like I'm fake running? Is that more demanding than walking and a good intro to running vs just running/jogging?
I hear what you are saying. Running gait is more sort of a lean-forward-and-push-off-with-toes type thing than a smooth easy walk. You can do that with short strides and medium-cadence and you won't go very fast.
Perhaps just transition into a run and then make a conscious effort to slow down, or go the other way where you walk faster and faster until your instinct is to change to a running gait and try to keep that pace.
The important thing is to try not run too fast "by accident".
Good luck