Where does it say moving silently requires the hide action first?
The Hide action is how you use Stealth in combat. It has its own rules. Remember in 5E 'hidden' is expressly defined as 'unseen AND unheard'. If you're hidden you must be both unseen and unheard, and in order to be hidden in combat you need to use the Hide action (and have the right environment to be hidden; such as being behind total cover, invisible, the enemy has his back to you or whatever).
Remember Stealth is both 'Move silently' and 'Hide in shadows'. Perception is both 'Spot' and 'Listen'.
If you want to sneak up on an Orc who has his back to you, you need to take the Hide action, rolling higher than his passive perception (and then move). Next round you can attack him from hiding.
If you're a Rogue of at least 2nd level, you can do this (Hide, and then move) and still make an attack as your action once you get there.
This is the whole point of cunning action. It lets Rogues hide and attack (or do other things like hide and dash, letting them double move while still moving silently, meaning they can move twice as fast as any other PC while hidden and remaining quiet).
Once you succesfully hide (take the hide action and roll higher than your opponents passive perception score) you cant be attacked unless your opponent makes a very lucky guess (and in some instances your opponenent may not even be aware you are there).
If your opponent wants to find you (assuming he is aware you are around somewhere) he must use his action on the Search action (and then roll higher than your stealth result with his perception check).
Example:
Jimmy the Wizard (Stealth +5) is in melee with an Ogre (Passive perception 8, -2 Perception bonus). Several rounds have passed, and Jimmy is down to his last 2nd level slot, and has only 3 hit points remaining. Things are looking grim.
Jimmys turn: Jimmy turns and starts moving backwards chanting a spell. [He uses his 2nd level slot and casts
Invisibility. He now moves 30' away from the Ogre. The Ogre cannot make attacks of opportunity against Jimmy as Jimmy is invisible and Attacks of Opportunity can only be made at 'a target you can see'].
Ogres turn: The Ogre blinks in surprise, sniffs the air and advances forward swinging his club in the direction he saw Jimmy turn towards, following the funny smell of the Wizards pouches, and footprints in the soft dirt left by the Wizard. [DM makes an attack at disadvantage as the Ogre cant see Jimmy anymore, in line with the Invisible condition]. He misses [the DM rolls a 2 and a 15].
Next round:
Jimmys turn: Jimmy smartly decides to go slowly, sticking to harder ground to avoid leaving footprints. He quiets himself, holding his spell component pouches still as he moves, and stifles his heavy laboured breathing, tiptoeing off towards the rooms exist. [Jimmy now attempts the Hide action. He rolls a 12, adding his +5 for Stealth getting a total of 17. The Ogres passive perception is 8, so Jimmy easily Hides from the Ogre]. Jimmy now moves 30' away from the Ogre, as quiet as a mouse.
Ogres turn: The Ogre is dumbfounded. The footprints he was following seem to stop suddenly, and he cant smell or hear the Wizard anymore. He stops and smells the air [The Ogre attempts the Search action. He rolls a 14, subtracting his perception bonus of -2, giving him a result of 12 vs Jimmys Stealth result of 17. The Ogre fails, and spends his action sniffing the air and looking around the room]. The Ogre has no idea where Jimmy is.
Notice how even if the Ogre rolled a 19 on his perception check (for a Perception result of 17, and just enough to spot Jimmy) he has already used his action to Search this turn, so he can't also attack Jimmy on the same round (although he can still move, so will probably advance to where Jimmy is). This gives Jimmy another chance on his next turn (which Jimmy gets before the Ogre can act again) to again attempt the Hide action before the Ogre can act. With Jimmys high Stealth score, its very likely that Jimmy again rolls higher than an 8 (the Ogres passive perception score) on the next turn, and again gets to sneak away from the frustrated Ogre before the Ogre can attack him all over again.
That is how it is supposed to work. There is an action economy at play here that you are houseruling away by granting perception checks and stealth checks (covered by the Search action and the Hide action respectively) as free actions (they're supposed to be actions, or a bonus action with cunning action or vanish and ther Hide action).
You're nerfing Rogues in particular by making cunning action [Hide] less useful than it is, and you're buffing an already potent 2nd level spell [invisibility] way more than it should be.