Actually, in skirmishes, it's rolling for initiative that doesn't make sense. In an actual real-world fight, assuming you don't put someone down right away, the fight itself is a series of exchanges of blows, some faster than the other. Unless it's a VERY lopsided fight in terms of fighting ability, each fighter will take a punch or a stab, and the other one will try to take advantage of the opening. In some cases, it's RAPIDEXCHANGE, back off and size up, RAPIDEXCHANGE, back off, etc. - but in few cases do fights last more than a few seconds; someone is usually hurt enough or dead enough to stop the fight.
Cyclic init makes more sense BECAUSE fights don't have "rounds."
And Delay doesn't make a darned bit of difference; thinking of it, you're going first before anyone else in the next round; there's no stop or start. Ever since we use init cards from Game Mechanics, this part has gotten fairly seamless.