One thing that has occurred to me is that a less dangerous variant may end up being more infectious in practice, as more infected people are either unaware they have it or are less incapacitated, and therefore are free to expose themselves to others more.  So this is one way that a less dangerous variant may overtake a more dangerous one, even if their inherent infectiousness is similar.

"Desperate"?  Seems unlikely.

This op-ed from the WSJ from a couple of months ago differentiates between "internal" immunity, apparently conferred well by the vaccines, and "mucosal" immunity, not so well.  So these positive tests among the vaccinated are largely confined to the nose and mouth, which limits their negative effect to the patient but still makes it possible to pass along to others.  Presumably this is what's driving the results you're skeptical of.