I don't think Honda have ever admitted a 'known problem', but some members here have had new racks fitted. It's certainly been a known issue on here.
As for whether it's safe, I think that it's more an irritation than anything. Once I realised it was doing it, it just bugged me. I can't remember anybody else thinking it was dangerous, or of the steering failing or losing power assistance suddenly, but you need to use your own judgement - after all, posters on here can't tell how bad it is.
It would be interesting to know if the problem with your Jazz is less evident in the morning when everything is cold. I found that ours was usually fine when the car had been standing and the engine bay was cold, and gradually got worse as the everything warmed up - usually around 10 miles or so.
Try it first thing tomorrow, taking note of the steering feel.
You need to decide if it is that notchy, rubbery feel, and the feeling of actual resistance to the wheel turning, or if it's just dead around the centre - that could be as simple as too much toe-out on the front wheels.
As for mine, I can only think that the thumping it had to remove the old wheel from the spline disturbed something - maybe moving the shaft upwards out of the rack, or disturbing the EPS motor brushes? I really don't know, as it was completely accidental. If the problem returned, I would do the same again - thump the steering wheel from the dash side with a soft hammer, see what happens.
