Being that this is a "subjective" exercise with little or no room for discussion - just a series of "subjective" ideas being offered and rebuked? - I had a thought for anyone else reading this thread and looking for different ideas. No offense to anyone else who is showing a lot more work and effort on their part. Personally ("subjectively"?), I like to simplify when I can.
Instead of defining each race with a preset of abilities, quirks, etc., which summarily categorize and profile every single individual of a non-human culture (think about it, you know it's true!), let the players pick their features first and then just name their race. Do we really need to limit our options because of someone else's preconceived notions of how an entire race is portrayed? Or wait for someone to house rule and customize new options to fit an idea?
So, for example, you can rule that every character gains a +2 bonus to one ability score of their choice, and a +1 bonus to a different ability score of their choice. Everybody gets to choose, and they get the same as everyone else. And less stereotypes! Problem #1 solved.
Next, pick your three racial abilities. Someone should compile a short list of the most commonly seen abilities and traits shared between all races. For example, a generic trait might get your choice of a +2 for any two skills of your choice, or proficiency in any two set of tools, or one of each. This could reflect your specialized background or upbringing. You can be a typical dwarf with a skill bonus in Craft and proficiency in Blacksmith tools, or the odd the dwarf who was raised differently.
Other ideas: automatic proficiency in two weapons of your choice, pick two bonus languages, and gain a free feat. (Yup, take that exclusive free feat away from the Human Variant so we can stop calling them "Human Variant" and just play "Humans" again, but without losing the free feat!).
If you want to take it a step further, introduce special traits, like Darkvision, that only apply to certain races but only if you can do it without excluding anybody. That means if the Gnomes can get Fey Magic that no one else can get, Humans (and all the others) should be able to get something unique as well. This is still part of the three picks each character gets to make, but they can only get one of these.
To me, this is much simpler approach to fixing something that is just annoying me but don't know how to fix it without reintroducing the same problems in a new way, or overcomplicating things and creating new problems. And if someone complains that they're missing a particular benefit or power, or they have fewer, well the trade-off is you get to pick everything. And maybe that's what some people want. Of course, this is all very "subjective" and not likely to be appealing to anyone but the person who thought of it. Enjoy!