Turian biotics are likely just as rare, if not more so. There has only ever been one shown in game, if you don't count the one in multiplayer. We have two of them. If you want to play a krogan with biotic powers, you are more than welcome to do so.
Biography/Background: Krusk originates from the streets of Omega where he lived in secrecy with his parents from the eyes of the Shadow Broker. His father was a previous agent of the Broker who handled the shady dealings, or dealt with agents no longer of use to him. When his father proved himself capable of killing anyone of high stature, the Broker turned the tide on him.
Forced into hiding, his father taught him everything he could about keeping light on his feet and out witting the enemy. Up into his early twenties he trained to prepare himself to combat the Broker, but Cerberus came stepping on the front door instead. Krusk lost his parents in the first raid; his mother murdered and his father held prisoner and executed. He escaped with an off-duty Alliance patrol with a heart full of rage and head of black thoughts, and it was in the alliance that he'd find his peace.
After signing on, he's served as a faithful soldier and lead a campaign of ten years combating Cerberus on the front lines.
Extra: After holding a decorated service record that impressed the council, he has been recommended for the Specters and joins them in the next few weeks... exactly on his bithrday.
That's still five powers, ammo counts. Also Flare was not an accepted biotic ability, it is far too powerful and by my reasoning, would wear a biotic out with just a few uses. The skill has a lengthy cool down even with max cdr.
M-5 Phalanx (for its simplicity and ease of access)
Biography:
When asked about his past, Hurk responds "I was hatched. I was named. I killed stuff." And it was true. But there is more detail to this skeleton story. Out of the clutch that his mother laid, only about 3 hatchlings survived, and he was the only hatchling with natural biotics. Hurk killed the other two when he realized he could get more food without them. When his father claimed him and named him Hurk, he trained hard for years after that. Hurk underwent his rite of passage, killing his Thresher Maw and earning the respect of his clan. But the peace and tension was too much for him. And as such, he spent about 4 centuries working and fighting with the Blood Pack, one of their most skilled mercenaries and Vorcha "tamers". But one day, something broke him: A job against a Salarian diplomat, flying in a cruise liner. The op went smoothly, the politician was assassinated, and the civilians executed. And that was what stopped him, and started him wondering: What was the point? Why was he alive? Why did he kill, why should he kill, and what gave him the right to kill? This new pondering sent him away from the Pack and away from his life of death and destruction until he joined the Krogan military in his 500th year. He ditched the armor and colors of the Blood Pack in favor of standard armor granted to Battlemasters, joined the Krogan Military, and performed operations on the right side of the law. But Hurk eventually felt the need, the blood rage within him that needed to be sated. And so he set himself up as a solo mercenary, taking any high-risk (practically suicide missions), high-pay jobs he could find, coming to shadow the reputation of the great Urdnot Wrex in his skill and efficiency. He fights with honor and mercy, showing respect to worthy opponents, and killing all his targets swiftly. And so his life went on. Until he got the call...