See, Sylvia, Jack, and Lucy were either originally going to have a story that they would've been adopted by All Might or by Endeavor because of Jack's quirk, but I changed it to Kouki because All Might was just.... idk, extra? and the poor children were scarred enough as it is, adding Endeavor would just make things ten times worse. However, Jack and Shouto still have similar quirks (he can control air's temperature, not just cause whirlwinds) in a sense, so it makes sense to me that Jack would intern with Shouto.