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I have it on a single rack & mudguard mount on each side of the fork (with the mudguard stays) with a selection of washers and a very long bolt. I'd rather have it on a separate mount but it's been ok for a few years, with quite a lot of shopping and stuff in it. On another bike I've used p-clips to mount a front rack, which also seems pretty solid.
Mounting the legs on the axle seems to me like an unnecessary layer of faff when you want to remove the wheel.
do you have it on a rack mount or on the wheel axle?
i suppose being able to take the basket on and off? (if you have an endless supply of zip ties)