Cogging will be a problem.
When you include cores in the stator of a radial-flux alternator, to avoid cogging you need to design the geometry of the magnets and the cores so that, at any position, you have the same total amount of flux through the gaps between the magnets and the cores. Otherwise there will be a torque to a different position where the flux paths will be shorter. (You can get away with "something close", but not TOO far from constant. See below.)
This torque can be very strong if your geometry is off, giving you the potential vs. kinetic energy equivalent of pushing a heavy cart, with good wheels and bearings, along a paved road with regular, and very high and deep, hills and valleys. But with careful design and accurate construction you can keep the hills low enough that it isn't a problem.
Once the mill is spinning all you get from cogging is vibration. But when the mill is stopped the magnets will have pulled the shaft into a position of low energy - "the cart is in a valley". To get it spinning the wind has to push it "over the top of the next hill", after which it will get enough kinetic energy from "rolling down the hill" that the wind can easily push it over the next one. You won't have drag from generation (except for eddy current losses - which are small at low speeds) until you reach cutin.
High-TSR blades produce substantial torque when they're spinning. But when they're stopped the bulk of the airflow is detached - the bulk of the blade area is "stalled" - and the part that isn't stalled is near the hub, where it has little leverage. So they generate very little torque - much less than if they were spinning near their design TSR.
The trick is to get the cogging low enough and/or the blade's stall torque high enough that the blade breaks the cogging and is spinning with the wind no higher than that necessary to bring a spinning mill to cutin. If you need more wind than that to get the mill moving, in low but useful winds it will just sit there - or if started by a gust it will soon be stopped by a lull. Low but useful winds are exactly when you most need it to be generating whatever it can. (If the cogging is too severe the mill won't start in winds lower than hurricane force, so it becomes a decoration rather than a power source.)
Radial flux machines, usually built by converting a motor by altering or replacing the rotor, also have cogging issues. But the stator core is manufactured by stamping - a very accurate process - so it's reasonably easy to arrange the magnets on the modified or replaced rotor to keep cogging low. Axial flux machines are more "freehand" and the geometry of the magnets not optimized to make cogging suppression easy. So even if carefully designed to avoid cogging, constructing them accurately requires working to tight tolerances, while a coreless design can be built to ridiculously loose tolerance and work just fine. Cogging is not an issue at all without the stator cores.
This is why we usually use coreless stators in radial-flux machines, compensating for the longer flux path by using stronger magnets. All the core buys you is the short flux path, allowing the use of weaker magnets and/or closer magnet spacing for higher output frequency and more power from a given area.
If you have a lot of cogging, and it's a polyphase design and has a lot of poles, all is not lost. By offsetting the magnets somewhat on different pole positions you can smooth out the transitions and reduce the cogging substantially (in principle you might even be able to eliminate it). You'll want to do this symmetrically on opposite sides of the rotor so you don't introduce a vibratory force trying to rotate the axle on the other dimensions, with the stator trying to move the way a coin behaves when finally settling down after rolling. (For a single-phase design you need to switch between the field going through the cores one way and going the other way, so there's an averages-to-nothing state between them. So you're stuck with high hills and low valleys, lowering them lowers your output, and the best you can do is optimize the slopes between them.)
