It sounds like a low-key racial trait that moderately "levels up" with the different tiers would work.
OR
If you want to keep it really simple, make sure every race has the same number of traits, and then just decide which one they get at 1st, and then which ones they get when they hit each of the tiers.
It is funny you mention this! While at work today I thought about maybe something like archetypes, where there are 4-5 racial features and you get one at first, another at 3-4, one more at 6-7, etc. and the last similar to a capstone ability.
This way the racial features truly represent the race, but do power-up with level so they are effective without being over the top.
Now, I just have to come up with them! LOL Here is a sample for Dwarf. (FYI I am not saying this is what I will do, as some of these features ARE powerful, but just to give people the idea.)
Dwarf (by level)
1: You have advantage on saving throws against poison, and you have resistance against poison damage.
3: By stealing yourself to take a blow you can use your bonus action to gain a +1 bonus to your armor class until the start of your next turn. (or maybe DR instead?)
8: You gain proficiency in one saving throw of your choice.
14: You gain temporary hit points equal to twice your character level after a long rest.
18: You gain advantage on all saving throws.
Thoughts?
Oh, and I am STILL very interested in learning what people consider the pinnacle core feature for each race. Come on, people! Let's keep this going.