Ovinomancer
No flips for you!
To expound on the issue with how stealth becomes being seen on a failed check, this is in part because 5e, and earlier editions that had such skills, put out stealth as an opposed check. You aren't contesting stealth against a DC set by the GM to achieve a goal, like some other skill checks in 5e (and based on the GM using this approach) but instead are directly competing against an NPC's skill rating for their "I see you" proficiency. As such, the rules themselves set up a contest between being not seen and being seen. An failure in a contested check is usually viewed as a win condition for the opposing side -- if you attempt to escape a grapple, for instance, failure means that the opponent gets what they want which is to maintain the grapple.
As such, stealth checks are set up by the way the systems works to have an obvious result -- that the opponent sees you on a failure. After all, that's what is arranged by the game, that you're trying to hide and this is opposed by the opponent trying to see you. After this, it's a matter of what happens when the opponent sees you? Quite often, raising the alarm is the usual result.
5e also doesn't really help if you try to make a soft move here, and say that the first failure just means the opponent notices something might be amiss. In this case, you can set up that the failure means the opposer hasn't clearly seen you, but has notice something suspicious. This appears opens up a larger set of scenarios, at first glance, but really doesn't do this because 5e lacks effective ways to deal with this. The atomic action resolution system of 5e - meaning you adjudicate the specific task rather than a broader intent - means that you can't effectively slip by the guard in this case using a different action. The rules don't support tossing a stone in a different directions to sneak past the guard while they go investigate that. Instead, you have a check to distract the guard with the stone, maybe a deception? Then a check to sneak, bounded by movement possibilities. Similarly, making an animal sound to convince the guard it was a non-hostile they caught wind of is another check that, on a success, results in a resetting of the situation, not a resolution of it. And, the combat engine prevents any stealth dealing with the investigating guard via violence. Not only is it highly unlikely that you can disable or kill the guard in one go, but you have the questions about whether or not you're rolling initiative for this, or if you're using the actual combat rules, and then there's the questions about whether this can even be accomplished stealthily at all.
5e's rule system functionally sets up the all or nothing stealth contests due to how they frame it as in opposition to the opponent's ability to spot you. 5e further has issues with resolving these scenes because it's resolution mechanics are atomic -- they deal only with a specific resolution of a physical task that is unconnected to anything outside that task (the mechanics, not however the GM frames the outcome). This results in really the only direct options for getting past guards to be stealth actions, as other attempts will usually just complicate the resolution and still will require a stealth action anyway. Combat is right out the window.
As such, stealth checks are set up by the way the systems works to have an obvious result -- that the opponent sees you on a failure. After all, that's what is arranged by the game, that you're trying to hide and this is opposed by the opponent trying to see you. After this, it's a matter of what happens when the opponent sees you? Quite often, raising the alarm is the usual result.
5e also doesn't really help if you try to make a soft move here, and say that the first failure just means the opponent notices something might be amiss. In this case, you can set up that the failure means the opposer hasn't clearly seen you, but has notice something suspicious. This appears opens up a larger set of scenarios, at first glance, but really doesn't do this because 5e lacks effective ways to deal with this. The atomic action resolution system of 5e - meaning you adjudicate the specific task rather than a broader intent - means that you can't effectively slip by the guard in this case using a different action. The rules don't support tossing a stone in a different directions to sneak past the guard while they go investigate that. Instead, you have a check to distract the guard with the stone, maybe a deception? Then a check to sneak, bounded by movement possibilities. Similarly, making an animal sound to convince the guard it was a non-hostile they caught wind of is another check that, on a success, results in a resetting of the situation, not a resolution of it. And, the combat engine prevents any stealth dealing with the investigating guard via violence. Not only is it highly unlikely that you can disable or kill the guard in one go, but you have the questions about whether or not you're rolling initiative for this, or if you're using the actual combat rules, and then there's the questions about whether this can even be accomplished stealthily at all.
5e's rule system functionally sets up the all or nothing stealth contests due to how they frame it as in opposition to the opponent's ability to spot you. 5e further has issues with resolving these scenes because it's resolution mechanics are atomic -- they deal only with a specific resolution of a physical task that is unconnected to anything outside that task (the mechanics, not however the GM frames the outcome). This results in really the only direct options for getting past guards to be stealth actions, as other attempts will usually just complicate the resolution and still will require a stealth action anyway. Combat is right out the window.