My 2011 FWD Rogue has 176K miles. But has been amazingly reliable.
I have a ticking noise from the front end about 2-5 ticks/ second at 15 mph, and it gets faster with road speed. It is constant whatever gear it's in, and continues out of gear and with the engine off.
I have replaced both front axles and cv joints, wishbone and ball joints, and front hubs and wheel bearings. Tires have been rotated to the rear. No difference.

I have to suspect the CVT, but it works perfectly.

Has anyone else seen this problem, or have a theory about the cause?

So it has to be between gearbox and road if it increases with speed and not with gear ratio or engine speed.

Already checked the brake 'shields'? Bound to be pretty rusty and mangled with that age and mileage, maybe one of them is touching.
Though that should be more a scrape than a ticking noise.

Pebble in the tire(s)? Oh wait, you said you moved them to the back and the noise's still coming from the front.

Noise still there if you lightly touch the brakes?

If your using the longer oil filter, try going back to the shorter oem version.