When discussing Sonic's characters most of us say 'they fun, but not exactly complex". Obviously Sonic games or comics will never attempt storytelling of Bojack Horseman, Steven Universe or Avatar Aang/Korra (all great cartoon BTW). With that said, not everything deep must be spelled out (I noticed few fascinating thing about characters from Bojack that show never acknowledged in depth).
So I believe that from right angle there can be find at least a little depth from Sonic's friends and enemies. For example
1 Eggman. He kinda comes off as very stereotypical evil scientistic, maybe a little 'adult child' comparing to Willy or Neo Cortex. But there is a very fascinating theme to most of his inventions (other than putting his face everywhere): Badniks, Eggman Land and Metal Sonic (series). What they have all in common? ....They are twisted joke, a corruption of something good. People like nature, here are animal-based robots (even with silly googly eyes). People like Amusement Parks, here's one that tries to kill you. And of course people love that blue rodent, let's make a deadliest robot based on him (Ironically his first victim, Amy, was Sonic's #1 fan).
When I heard somewhere that Robotnik was mockingly called Eggman, and he took it as his official nickname, I though it's a stupid retcon to smooth West/Jap connection. But that actually fits perfectly with his characterization : people found this name funny, so he took it. Now he build tons of deadly weapons and calls them Egg-something. So suddenly something that was funny to you is now associated with death and destruction. (Mind you, that is his intention, not official outcome).
And there is even more baggage if you look at Preboot Archie Eggman, but that's for another day.
2 Metal Sonic. I wrote whole fic around this concept, but basically I think Metal Sonic is insane. Or at very least he was in Heroes. "There can be only one Sonic" is a famous quote from Sonic's OVA movie. Metal's entire existence is based on defeating one person he hates, yet he's just Sonic's knock-off. Solution? Convince yourself YOU'RE the real Sonic, and fleshing is somehow your loathsome copy. Now that's already stretching reality. Only worse thing would be if you LOST to that copy. And again and again. That could push you to do something drastic, like becoming a giant metal dragon or something. In other words: he's put together the wrong way.
3 Omega. He's not the first Eggman robot to rebel. But he's the only one still in process of that rebellion. It's funny how long time ago he decided to kill Eggman, but so rarely does anything towards this goal. Could it be that somewhere deep in his head he doesn't want to fulfill his goal, as that would bring him to his biggest fear: lack of purpose?
Omega's reason to rebel sounds silly: he left without orders. But robots live to serve, he needed some kind of orders. So he got so desperate that first two organic he meet suggest him a goal, he took it in a second. He even follows then, while not officially a servant, he's always a sidekick to Shadow or Rouge. Rarely he goes on his own to destroy Eggman's robots, but he's totally not in a hurry to finish it. Because if he's done, he would be back to that room Rouge found him: without a purpose.
OR IS HE? He was sealed with Shadow after all. And Mephiles said Omega is the one to capture him in the future. Maybe goal of destroying Shadow is still in his head, but was overwhelmed by hatred towards Eggman. Maybe Omega doesn't won't to accomplish his goal anymore, because then he would be left with only one purpose in life: destruction of his best friend.
Well, those are my ideas and observations. Anyone else has his own ideas how Sonic Cast can be a bit more complex then we give them credit for?