When you’re putting input into the bike at lean, it won’t wobble. The wobble is a progression that starts with a lightly loaded front tire, and every bike I’ve ridden with a good quick front suspension geometry will wobble in the right circumstance. A steering damper will kill the progression of a wobble, but if you’re accelerating the front can still give a wicked shake on a bike with a damper. Enough to loosen the front brake pads, smash thumbs, etc.

When racing, if you have a hill crest that you’re accelerating over and you set the front down after the hill, it’s common to get a good shake. You learn to ride through it.