By machined alloys are these the new black/silver ones? If so do not use a brush only a sponge, brush scratches the black coating.
I’ve got the set of three Wheel Woolies, and they’re very safe as they don’t have bristles like a wheel brush does - they’re made from a very soft wool type of fibre. I’d not use a sponge on wheels or paintwork - grit gets trapped between the sponge and the surface you’re washing, resulting in swirls that’ll be particularly visible on dark coloured surfaces.
I use all three of my Wheel Woolies, as they’re good for other parts of the car as well as wheels, such as honeycomb pattern grilles, painted brake calipers, the underside of the sills. They’re really good at cleaning the wheel barrel behind the spokes of your wheels too. Admittedly, a set of Wheel Woolies aren’t cheap, but if they’re looked after (thoroughly cleaned out after use and left to air dry before putting them away) they’ll give many years service. I’ve had mine 2-3 years now and they get used every 7-10 days and they’re going strong and look pretty much the same as the did when they were new.
If you don’t want to invest in a set of Wheel Woolies, you could try a dedicated microfibre wheel wash mitt - I use one of these mitts to wash the fronts of my wheels and the recessed areas between the spokes, and use the Wheel Woolies to wash the wheel barrels;
https://wo-wo.co.uk/collections/wo-wo-car-detailing-products/products/microfibre-wheel-wash-mitt