You are making up more rules. I asked last time for a page number... and you did not provide one.
So lets try again. Please provide the rule that says 'skill use requires an action'. (Even 'generally')
You are making lots of assumptions....
Here's the deal, the 5e PHB isn't written that explicitly. There's a dirty little secret to the system that those who played 3.5e and 4e (and especially if you followed the D&D Next playtests) extensively know: The designers barely changed the game from previous editions. A large portion of the game is literally the 4e rules exactly. But with the explicit language removed. People complained that in 4e everything said "You can use a Standard Action during your turn to do X". "Standard Action" sounded too technical. Some DMs got annoyed that the rules were TELLING them that it ALWAYS required a Standard Action when they wanted to rule that in THIS particular situation it didn't take an action.
So, you won't find explicit wording in the book saying that "skills take an action". On the other hand, you can find various pieces of evidence. Anything that takes a significant amount of effort takes an action. Most of those are listed in the book: Hiding, Attacking, Dashing, Disengaging, Casting a Spell, Helping, Reading, Searching, Using and Object. It also says under that same section that "Your character can do things not covered by the actions in this chapter, such as breaking down doors, intimidating enemies, sensing weaknesses in magical defenses, or calling for a parley with a foe. The only limits to the actions you can attempt are your imagination and your character’s ability scores. See the descriptions of the ability scores in chapter 7 for inspiration as you improvise." (p 193). So, you can spend your action to do various other things in combat. It isn't a coincidence that almost all of those things are skill or ability checks.
Thus, the implication that most things you can do with a skill require your action. But worded vaguely enough to allow the DM to rule otherwise in certain corner cases. It should be noted that the rule in 4e was that all skill checks in combat required an action. It isn't a coincidence that we ended up with a vaguely worded version of the exact same rule.
I never said you can't... I said the rule did not explicitly give you the mechanics for it.
I believe you *can* move stealthily...... even if you Hide first. You seem to believe you can't move stealthily unless you Hide... I just point out that your claim is tenuous since Hide *never* gives permission for movement.
Hide never gives you permission to move...nor does it give you permission to die, breathe or speak. In fact, it denies speaking saying that you immediately draw attention to your location if you make noise. But not giving you permission to do so isn't denying you things you can already do.
The rules say, essentially: If you'd like to not be seen or heard then take the Hide action to do so. In order to Hide you use your Stealth (Dex) skill to determine if people see or hear you. You make a Stealth roll and if you exceed the Passive Perception of the people around you, you've successfully escaped notice. But you can only do so if a creature can't see you.
It should be noted that those are the rules for Stealth and hiding precisely from 4e. But, once again, with much more ambiguous wording to give more wiggle room to the DM.
In 4e, the rules were much more technical, but basically said the same thing:
1. In order you use the Stealth skill to hide, you must have superior cover or full concealment from an enemy. Invisibility is defined as "full concealment". It explicitly says you can know the location of an invisible creature during combat because they still make noise unless they've made a successful Stealth check ("You can’t hide from a creature that can see you", "An invisible creature can’t be seen, so it can always try to hide" p. 177). Superior Cover is explained in a large amount of detail using line of sight on a battle map of squares which is missing from 5e. But 4e explains that you can still see someone who has partial cover automatically because they aren't attempting to hide and you still have line of sight to them. You can see everything you have line of sight to. You can hear everything automatically unless they use Stealth to be quiet ("An invisible creature can’t be seen, so it can always try to hide. Signs of its passage might still be noticed, however, and it still has to stay quiet." p. 177 implies the same thing is still true. You can be invisible but people can hear you and notice "signs of passage" unless you are "hiding").
2. You make a Stealth check vs the Passive Perception of everyone who could see or hear you. ("To determine whether such a creature notices you, the DM compares your Dexterity (Stealth) check with that creature’s passive Wisdom (Perception) score" (p. 177))
3. You make Stealth checks as part of a move action (This is different in 5th, Hide is listed as an action you can take in combat)
4. Your Stealth ends whenever you a) Make noise b) Make an attack c) No longer have cover or concealment to the person you're hiding from (In other words, "if you make noise (such as shouting a warning or knocking over a vase), you give away your position", "You can’t hide from a creature that can see you", "if you come out of hiding and approach a creature, it usually sees you" (all p.177), "If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses." (p.195))
5. If you move you have to make a new Stealth check with a penalty for how fast you are moving. (This is different in 5e. There is no penalty listed for moving and it doesn't say to make a new check when you move).
The rules for Stealth/Hiding are basically identical with 2 changes.
As for whether it is possible to use "Stealth" without taking the Hide action. This is was the Hide action section says: "When you take the Hide action, you make a Dexterity
(Stealth) check in an attempt to hide, following the rules in chapter 7 for hiding. If you succeed, you gain certain benefits, as described in the “Unseen Attackers and Targets” section later in this chapter." (p. 192)
Thus, it implies:
1. If you don't take the hide action, you don't get the benefit of being an unseen attacker or target.
2. If you don't succeed on check you don't get the benefits either.
It also says under the Unseen Attackers and Targets section on page 195: "If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses." This defines "hidden": "both unseen and unheard". The rules on p.177 and p. 192 say that in order to Hide, you take the Hide action, which makes you "hidden".
We can make a inference from all of that saying "If the rules say you get those benefits from taking the Hide action then there shouldn't be a better way or one with less cost to get those benefits unless we want the second option to be imbalanced."