Wahoo support was great and quick. They request a picture of the sales receipt, the serial number plate, and a 30 second video (15 seconds pedalling, 15 seconds coasting). They got back to me in less than 24 hours advising that this is somewhat common. Here is their reply:
Thank you for sending that video through. I reviewed the video with our technician and the noise you are describing is normal for a new KICKR Core out of the box!
The rhythmic sound in the video is caused by the print on the belt passing through the tensioner pulley. That noise will vary slightly by unit and typically will get quieter with use as the belt wears in. I do not believe there is any cause for concern on this unit, of course, if the noise gets worse or is bothersome after a few rides please let us know.
I expressed my surprise that they’d have such print on the belt if it made noise, that is a design issue. Also asked how long to wait for the belt to “wear in” before considering it a continual problem and getting it further dealt with. They replied back within minutes saying to give it a month (which will be plenty of miles/hours of use in my case) and reach back to them if it is still there.
Regarding the thought of whether this could be related to the cadence issues @Jeff_Horrocks mentions, after thinking about it, I seriously doubt they would be related. Unless this click is actually coming from a mechanical part in the torque/resistance system, it would not be related. Cadence is a software derived answer based on the Kickr sensing the reduction in force twice per revolution of the pedals. Simply a software byproduct.