Actually it seems to me more that ANY species can become an Alpha... but needs the right conditions in order to do so. Bewilderbeasts and other leviathan class dragons have the easiest time of doing it... but other breeds can become alpha also because it's not just the control aspect which is important... its an over all social aspect.
Yeah. It's explicitly noted in supplemental materials that Bewilderbeasts are not always alphas. They have to earn the title like any other dragon. It's just that they and Red Deaths have a very easy time at it due to size and the control ability.
Which makes me curious; as an alpha, does Toothless now protect Berk's dragons from that control because mentally he is the alpha? So, even if he can't project that call he still provides psychological defense against being lured away? If not, Berk's dragons are really going to be dependent on their riders for protection the same way Hiccup protected Toothless during the fight.