Yes. Pathfinder 2e has a good one.

Rolling a nat 1 or 20 doesn't mean Critical success/failure. It means it moves the success status up or down one: Critical success, success, failure, critical failure. In addition, that game also specifies that a critical is also achieved by your result being +/- 10 of the result.

So if you're attempting a DC 35 check (arguing with a god, let's say) with a +2 mod, a nat 20 would get you a result of 22, a critical failure. But a nat 20 bumps it up one success, so you get a regular failure. Whereas if the DC was 25, a 22 is still a failure but your crit means it's a regular success.

This has middling applications in D&D 5e, though. PF2e's DCs and skill bonuses are not constrained by 5e's Bounded Accuracy. So they can vary a lot more. In D&D's case I had to pull pretty much the highest possible DC the game suggests so there's not a lot of use cases for this. But it's still a better system for including criticals on skill checks. And this is why 5e doesn't have them normally.

There is the option for removing trivial skill checks, as mentioned elsewhere in the comments of this post, but most players I've had want to roll for the small stuff. Just expecting you succeed gets really boring after a while. Not to mention a lot of us bought shitloads of these clicky math rocks and want to use 'em. So while that's an option it's not one that I'm a particular fan of. Advantage I'm also not a huge fan of as it then feels like it cheapens advantage itself. I use both advantage and disadvantage sparingly in my games and have outright banned Silvery Barbs at my table for that reason. When you get advantage or disadvantage from something I like it to feel like an "Oh fuck" moment. A friend helping you out in a time of need or an something catching you completely off guard. My idea would be confirming critical failures.

For combat I understand a simple natural 1 equals a failure. That is under pressure and yes you can choke in those moments or just be bested by an opponent. But for skill checks you're proficient or an expert in during a non-pressure environment or situation it makes no fucking sense. Cut that chance down by making them confirm it.

Natural 1 on a Proficient Skill = Re-roll the d20. If you roll 10 or below then you critically fail. 11 or above and your result is treated as a simple 1 instead of a critical failure.

Natural 1 on an Expertise Skill = Same as above but the failure bracket shifts down to be 1-5 for a critical failure and a 6-20 for a simple 1.

That's how I'd run it anyway. Maybe shift the failure/success brackets but the same basic set up.

For most skills, there low level human equivalents in the real world who will never "choke under pressure" once when doing the thing thousands of times throughout their life. When we're talking about one of the heroes of a tale that are also "the best of the best", I think it's ok from a literature, fantasy, or gameplay standpoint for them to have a 100% success rate despite the fact that a failure risk would be possible in the real world. This is doubly true (DM point of view) when failure would be uninteresting or mess with suspension of disbelief. If an ace pilot is trying to fly through a bad storm to land where the firefight is going to happen, he bloody well makes it. I'm ok with "success with complications" on a 1, but the complications should be fun as well. You land ok, but the wind that hit at the last minute caused some damage to a wing. You might need to find another way out" or even "unfortunately, you weren't able to fly evasively enough because of the buffetting winds, so they know you're here.

Nobody wants Skyrim syndrome, where a master thief gets caught pickpocketing someone (we Bethesda players do something called save-scumming to keep the immersion). I used to go to a pickpocket show at the local renfair and the performer never got caught. And he was not a "master thief".