Geez that's nothing. Back in the 80s when I used anodized rims they'd look like that after a week. It's irrelevant. If the brakes are pulsating, are your wheels out of true? If so, true them or get them trued. It also helps to sand the brake tracks lightly with about 220 grit sandpaper. That will remove anodizing, but it's already gone. The anodizing is just for aesthetics. Marketing used to insist otherwise, but it's bs.
There's no need to replace the wheels until the rims have been trued many times, and the spokes have started to break or gotten excessively uneven in tension. Even then, the conventional repair is to rebuild the hubs with new rims. There's a reason some of us who used to work in bike shops BITD have built hundreds and hundreds of wheels. Re-rimming used to be almost like getting new tires. Rims get old and bent, and need replacing.
However, times have changed. It may be cheaper these days to buy some premade replacement wheels like those Velomine M13 things. A bike shop in this century is likely to charge more than that to rebuild your existing wheels.
That said I'm not at all convinced you need new wheels or rim at all.
On the other hand, if you just want some new wheels that's perfectly understandable. Either reuse the hubs you have, or get new ones, but stick with freewheels IMO. 126 cassette stuff has been gone too long. Freewheels are still around. The bike could be converted to 130 but that would take some effort.
Last edited by Salamandrine; 06-12-20 at 07:53 AM.