https://community.playstarbound.com/resources/racial-intros.5468/

The Racial Intros mod starts to address this. It's pretty rough around the edges though. (Not knocking the mod, just saying it'll just take a tonne of work to polish up 6 additional intros to the level of the vanilla intro.)

It'd also be nice to have semi-random race-specific faction-specific side missions with character-specific reputation, e.g., do a quest series to help Apex rebels, but if you complete it, that character gets locked out of the quest series to help Big Ape. Maybe even have a faction's villages become hostile to you based on reputation, e.g., Apex cities default to hostile to you if you complete too many Apex rebel quests. This would require a tonne of work, but could add quite a bit of replay value to the game.

I like having a single unifying mission series in the game, but I do think it should be limited to one playthrough per universe. How I envision this could work would be Ester gives everyone the initial quest line (fix your ship, scan the outpost). She also gives everyone the core quest series until some character defeats the ruin. But, she should skip the individual race quests once each is finished. For example, Character1 starts the new universe, repairs his ship, scans the outpost, and does both Floran missions, but he dies afterward. Character2 is created, does the repair and outpost scan missions, but then skips straight to the Hylotl mission series. This progression continues until some character destroys the ruin. Make a permanent statue of that character on the Ark, and Ester no longer gives the core quest series, because (in that universe) the Ruin is no more. Subsequent characters should still get the repair mission from her, but then they can skip straight to the vault missions and the (hypothetical) racial missions, or just plain old exploring.

I'd love to do a mod implementing that, but honestly it'd be an enormous amount of work and I probably won't ever get time for it.