So I should probably actually properly explain my takagi is matsuda theory(/AU Idea)
My brain had this idea about 10 years ago when I was first watching the show, but I didn't interact with fandoms at all back then so it kinda just lived in my head taking up space.
As we all know, Takagi and Matsuda look similar. Similar enough that Takagi can disguise himself as Matsuda by accident.
And for the character with the 5th most screen time in the entire show, we really don't know much about Takegi's life before division 1.
With Chiba, Sato and Shiratori, we know a bit about their life before joining the force, with all 3 of them having flashbacks to their childhood at some point in the show.
And while we don't know much about megure's life before the force, we do know some stuff about his life before the show. We've seen flashbacks to his early days on the force and we know how he met his wife.
But for Takagi's life before division 1, we don't really have anything other than general comments (for example, "I was only in elementary school back then" when megure mentions a 20 year old case in the desperate revival arc).
And as for his life as a division 1 member before the show started, all we know is that he joined sometime after Matsuda's death but before Shinichi solved the airplane case. And that he was mentored under Detective Date.
For a character we see so much of, we know suspiciously little about him, we don't even know what inspired him to become a detective.
But what if there's a reason for it?
And so I propose to you my probably wrong but definitely fun to think about theory:
what if Takagi and Matsuda are the same person?
What if Matsuda survived the explosion, but developed amnesia as a result of his injuries?
What if, after the funeral, Megure got a call from a hospital, asking for help identifying a man with no memories and a partially destroyed police ID?
What if Megure had to make a decision: whether to tell his subordinates that the man they grieved survived, but may never remember them, or to help him start anew from a blank slate.
What if Megure chose to keep him close, in the hopes he'd start to remember things as time passes.
Memories, skills and knowledge are all stored in separate parts of the brain, so even if he doesn't have his memories, it's not impossible that he'd retain some of the skills necessary to still function as a police officer
Also I know there is a 3 year age gap between Takegi and Matsuda, however it wouldn't be the first time someone had a fake identity younger than them cough cough Shinichi cough cough ai cough cough Shuichi cough cough
(it would be funny if the age gap happened because someone asked how old he was, and he panicked and picked a number that felt close enough, and by the time megure found out, it was too late to fix it)
Anyway, this is just a silly theory, but it's definitely fun to think about, and it would make for a fun AU.