Not too spoilery at all! Thanks for asking, actually. 🙂
There are various reasons they don’t. They major reason has to deal with my HC on the purpose of colony markings in the current timeframe of Parable, the games, etc.
Long explanation short, it deals with pride in your ‘home’ and the show of loyalty to that home. It’s like saying ‘this is my home no matter where I go’ as well as ‘if I ever need to, I will protect my home to the death.’ Sure, they are all one people under the Hierarchy, but the reasoning still kinda stuck, only altering to fit the unified turian people. It’s a lot like the idea of it’s better to fight with something in mind than just because you’re told to. Having a visible representation of home helps turians hang onto what they fight for. (A turian doesn’t always have to wear the colony markings of the world or colony they were born)
To explain why Aeson has them: He sees the Wraiths as home. The design he wears isn’t for an actual location, but a group of people. A family. His father didn’t have paints before the Wraiths and seeing his father be accepted despite his history made Aeson proud of his home. He may not have much, but he gladly gives his loyalty and trust to the Wraiths (though, granted, it also has a lot to do with who actually leads the Wraiths, but they wouldn’t be who they are without their three leaders anyway).
Now, for Damocles: He rejects any form of loyalty against anything but himself. His father carried marks of his home on Palaven and, yet, his father can’t just go back without hiding because of the way the Galaxy now views Garrus. Damocles refuses to paint himself as anything belonging to a people that’d just as soon turn him into an experiment or crime against nature than accept him too. He cannot find any other reason to wear any Hierarchy paints. He doesn’t wear the Wraiths’ paints because – we all know him – he’s rebellious. He’s not loyal to a merc company, he’s loyal to his family and above all, himself. There’s a difference there.
Cassia: Cassia will actually use temporary paint when off Virmire (and sometimes while on it). She has a bit of the same thinking about permanent Hierarchy markings as her brother, though she’s not as angry about it. She looks at it all as a way to be free of any real obligations (even if it’s it just cultural) while her life is still so fluid and ever changing. She knows where her loyalty lies, so she doesn’t feel the need to permanently mark herself. That, and she’s actually pretty skidish about getting permanent marks. She’s a bit afraid of the process so she’d much rather have to paint them on herself without going through the permanent inking process. It’s actually something pretty common for turians that live more on ships than planetside, so she isn’t looked on with prejudice or suspicion when she’s on places like the Citadel or Palaven while she handpaints markings.