even if L successfully solved the kira case and had Light executed, lets be real, he wouldn’t last that long. For the sheer fact that nothing would ever be an interesting as Light Yagami ever again. Even in s platonic angle, L is a detective first and foremost because it cures his boredom- once he’s had a taste of something that un-boring, do you really think he could go back to the same old cases? Even the most interesting of secret plots could never compare to Kira, to Light. He would spend the rest of his energy searching for someone on his level again, someone to make things interesting- always to no avail. He couldn’t go on after the Kira case.