In design, you need rules. Even if you deviate from them sometimes. The snapshot rule provides some measure of consistency. Without it, things get really weird, and tags have to be reconsidered every time a new anything comes out that adds to the lore of individual characters.
If characters were not snapshots...
Wedge, K2-SO, Sabine, Cody, and every Han would be Empire. And all of the Hans plus Cody would be Imperial Troopers.
Asajj, Dooku, and Vader would be Jedi.
Most of the Empire leaders would be Galactic Republic.
Now, as to the notion that all dark side users should be Sith and all light side users should be Jedi? No. No, that's not it at all, and we just had an entire movie on why that notion is wrong. Also, it would mean the Nightsisters would be tagged both Jedi and Sith, because they draw on both sides of the Force, favoring neither.
"Jedi" and "Sith" are religions. When Ahsoka leaves the Jedi Order, she abandons that faith, though she takes the training and some of the philosophy. The Nightsisters and Kylo have little to do with either of those religious orders. Visas as she appears in KOTOR has turned her back on both of them.
Faction segregation is important to making a diverse game. Break down those walls too much, and you go from multiple viable factions to a few titan-scale toons that are viable.