The axle has splines which transfer torque to the hub. There is a little clearance so the two parts can be assembled and later serviced if need be. A little clearance also allows parts to be more durable. After reading this thread this sounds like the countless other threads involving very similar parts on other cars and trucks. The click shouldn't hurt a thing and can be solved with grease until the grease dries up or gets slung out of the hole and the click returns. The parts can also wear enough so that nothing sticks and the sound disappears.
A few years ago Ford had this problem with driveshafts, exacerbated by the fact the metal they used would rust and fuse the parts together until they broke free with a clunk and bang loud enough to make the driver think they had been in an accident. After a while, they would wear enough and the problem would fix itself. Greasing it also helped but prolonged the time it took for the surfaces to break in.
Haven't seen these parts on the M3, but they are pretty robust un the Model S. Ostensibly someone who mostly regens may never have the rear suspension apart and these are supposedly designed to go 1,000,000 miles or more (which we are hearing a lot about today with the new battery news). If so, that's a heck of a bearing ... .
I would actually have greater concern about the axle nuts being over-torqued to silence a click and causing premature wear elsewhere. My guess is that this has a bearing pressed into the carrier assembly and not many of us have a bearing press in our garages anymore.
I recently got this click fixed for driver side rear wheel. Talked to tech about it, but what he says did not make any sense. He said, some about the washer there, and when the axle is moved relative flange, washer is sliding/clicking because of relative motion between those.
There is not supposed to be any backlash between wheel hub/flange and the axle splines. Backlash is never good in any drivetrain. There is a reason that axle nut is tightened pretty hard on pretty much any car(front wheel or rear wheel drive), and it is not a floating joint. Its not unusual to see some backlash in the differentials(and tolerances are specified), but no backlash is allowed/expected between the axle and hub. If there is a backlash, the axle splines had to deal with impact force, instead of simple torque transfer. You may not see failure right away because of this backlash, but eventually it will damage Hub splines and/or shaft splines.
Not sure where you got the idea that the backlash is ok between these two components. These are not designed to have relative motion between axle splines and hub unlike the gears. It is not even recommended that you put the lube in between.
Lubricating Light Vehicle Axle Shafts