What's the problem with the backflip?
Have none of you heard of swashbuckling? A flashy fighting style, full of showing off and exagerated motions, very intimidating. Intimidation can be very effective.
Plus their physically capable of it.
Plus, Sp'lasers may have been prototype weapons available for Spartans since soon after first contact with the Covenant. Granted they wouldn't have been available at Cole's liberation of Harvest but I have no idea how long the campaign takes in the Halo timeline. So there's not really a problem with them being there.
EDIT: Halo has always sacrificed realism for fun and balance, the specs of various units, weapons, and people are different in-game and in-canon.
And Bungie would never endorse a Halo story that wasn't true to canon.
"This facility has a successful utilization record of 1.2 trillion simulated and one actual.
It is ready to fire, on demand."
-2401 Penitent Tangent