Actually, Shukichi solved the case in his intro before Shinichi/Conan (File 847–File 849/Episode 731 and Episode 732)—it was his words that ultimately led to Shinichi/Conan solving the case. Masumi could've described Shuichi as strong and Shukichi as smart because Shukichi wasn't exceptional in the physical realm, rather than because Shuichi wasn't as smart as Shukichi. If Shukichi just solved both cases on his own, then Shinichi/Conan would have nothing to do, right? I don't think Gosho wants that. Shuichi/Subaru giving Shinichi/Conan the hint to solve a case—just like Shukichi did—(File 812–File 814/Episode 690 and Episode 691) was followed by an action sequence, and Shuichi/Subaru didn't follow Shinichi/Conan, Ran, Sonoko and Masumi to the scene. Not many people can reason on par with Shinichi/Conan, and let's not forget that Shuichi/Subaru also reasoned on par—not ahead of—with Shinichi/Conan (File 638–File 640/Episode 510 and 511; File 664–File 666/Episode 542 and Episode 543), just like Shukichi did in File 899–File 902/Episode 785 and Episode 786. That's one time ahead of and two times on par with Shinichi/Conan for Shuichi/Subaru and one time ahead of and one time on par with Shinichi/Conan for Shukichi.
Gosho keeps dragging this middle brother question on, thus keeping us in the dark about Shukichi's relationship with his family. We don't know about the extent of his knowledge about his brother's or their mother's situation.
He probably is the DC equivalent of Mycroft Holmes, though—him wanting to end that match with Tanimori early so he could go to his wife makes him differ from Mycroft, in that respect—he prefers not to engage in the activities that his brother and sister do. If he's kept Yumi waiting so long, then his family probably experienced similar things. Still, their reaction was probably the same as Yumi's—annoyed, exasperated and frustrated, but ultimately, he was worth all that.