May I ask, why do you think everything needs a "precedent" to justify a houserule?
Not everything, these two things.
Why? Because they are basic mechanics. Every edition of D&D had to devise a system to determine how often a class feature would be used and how it would give a "bonus" if a die was rolled to determine success. 5e adopted a basic design philosophy to address these two mechanics, playtested them thoroughly, and decided that they added to a fun experience.
Can you be creative with these basic mechanics as well? Sure, but I don't see any added value. Personally I would pick an existing class feature in the PHB that accomplishes the desired frequency/bonus, copy that, and move on. The interesting stuff is everything else that you have done, not the choices you make with basic mechanics.
Well, I think of it like this...There is natural skill and there is learned/trained/practiced/improved ability. These are "race-classes" after all. The "genetics", if you will, need to be taken into account in the base class. For gnomes and halflings, that most definitely includes small size.
So they, naturally, gain advantage on stealth/hide checks. Any halfling, any gnome, from anywhere, because they're small and easily overlooked (not to mention the typical story fluff of being difficult to find/hidden communities, etc...) is more likely to successfully hide/stealth than other races. That's advantage.
Here's where the PHB has done it differently. The PHB elf has keen senses. I would assume that is genetic. But they have proficiency bonus to Perception, not "always on" advantage on Wisdom (Perception) checks. From a world-building fluff perspective, the goal has been accomplished. And it respects the basic mechanics at the same time.
What is the intent of advantage/disadvantage? For the DM or player to create situations where it would take effect, not for it to be "always on". Does it break or unbalance anything?
No. Is it fun to roll two dice every single Stealth check? IMO not really, because there is no point to Hide in any clever way.
Now, something like the burglar or any halfling or gnome that takes proficiency in the Stealth skill, as per normal rules, then gets to add proficiency bonus to that roll. That means, yes, they will be successful even MORE often than your halfling-/gnome-about-town (and almost certainly on the second roll from advantage). That...just makes sense to me.
As a general parameter for coming up with these kinds of things [again, and always, all of this is "for/to me"]:
Rules/crunch sense + Story/fluff sense = "Yep! That's goes in."
So you want to make these guys super-sneaky, that's cool. Let's do the math.
"Always-on" advantage + proficiency at 1st level (or whatever low level the PC gains proficiency): +1 to +5 (average +3) for advantage, +2 for proficiency = +3 to +7, +5 average
Expertise at 1st level: +4 - not a significant difference, plus the PC can still look for situations that give him or her advantage
"Always-on" advantage + proficiency at 20th level: +1 to +5 (average +3) for advantage, +6 for proficiency = +7 to +11, +9 average
Expertise at 20th level: +12 - is that a significant difference? Maybe, but we don't play 20th level, so it should be good enough. Plus the PC can still look for advantage.
That seems...well, completely arbitrary. What is "inelegant" about it? How can rule even be "inelegant"?
What I mean by inelegant is that it comes off the page as a square peg trying to be fit in a round hole. It immediately prompted the question in my mind, "Why?". That is the only reason I asked these questions, because I want to read more pdfs from you in the future and not have to ask myself why you are making these choices. So thanks for answering.
House rules that scale without you having to write, "At X level, you have one more use, and at X+4 level, you have even one more use!" might be called efficient, maybe that's the word I was looking for.
But, in comparison to Expertise, expertise just grants you double proficiency bonus. You are better at, literally "have expertise," with skills of choice. It is my view/opinion that halflings and gnomes are naturally better at stealth/hiding. That's not just "extra trained," i.e. doubly proficient.
I would contend that the resulting outcome of the rule should take precedence over the connotation of the word "Expertise". You wanted a super sneaky guy, you get a super sneaky guy. No reason to go beyond that.