The Hide action is one way to become hidden. Being invisible, or being in total darkness achieves the same effect, without the need of the action. You are effectively hidden while invisible. That puts it back to "guess the square".
There's a huge gulf between "can", "might" and "automatically does". There's no logical reason for you to know a stalker's location without a roll once the creature moves following discovery. I get D&D sucks for simulation, but this throws even my V-tude. You only get to know it's location at the time of the attack, not forever until it hides again.
Wrong. Hidden is UNSEEN AND UNHEARD. "If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses." PHB Page 195
The Hide Action only lets you become UNSEEN. "You can’t hide from a creature that can see you,
and if you make noise (such as shouting a warning or knocking over a vase), you give away your position. 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." Page 177
You are not "effectively hidden" when invisible, you are UNSEEN and need to do something else to be UNHEARD to become HIDDEN. The Invisibility Condition states: " An invisible creature is
impossible to see without the aid of magic or a special sense.
For the purpose of hiding, the creature is heavily obscured. The creature’s location can be detected by any noise it makes or any tracks it leaves.
You simply do not understand that the following things are DIFFERENT:
1. UNSEEN - means the enemy cant see you. To be unseen you need to have something that blocks vision to you, like heavily obscured space or invisibility. It is a PRE-REQUSITE to attempt the HIDE ACTION.
2. UNHEARD - means you are not making any sound at all. This usually requires a Hide check or Stealth check as appropriate to the situation. Silence spell or elven boots work. You need to do this in some cases combined with the HIDE action to become --->
3. HIDDEN - is UNSEEN and UNHEARD. You need BOTH to be hidden. Hidden is poorly defined though, you can be unseen and unheard and still give away your position, say by standing on a soft surface where you foot impressions are seen.
4. INVISBILITY is a CONDITION that you gain or lose. It means you are UNSEEN and impossible to see. You can use this to take the HIDE action. See page 177. You can be detected if you make noise or leave tracks, see Invisibility Condition. Being detected means you are still UNSEEN but your general location (the space you are UNSEEN in) is now known. You still get to attack with advantage and be attacked with disadvantage.
None of those terms are interchangeable, they are distinct.
Attacking ALWAYS gives away your location. Your location stays known until you become HIDDEN again, which means UNSEEN (no vision to you) and at least UNHEARD ("Signs of its passage might still be noticed, however, and it still has to stay quiet.")
Invisibility means you are always UNSEEN but does not grant UNHEARD, the other requirement to being HIDDEN.
An invisible stalker (and other invisible creatures) make noise as they take actions. The invisible Stalker description says so. It makes VERY LITTLE noise, stealth check +10. There is no "take 10 rule" anymore, however there are PASSIVE check rules. If players want to use a passive check (perception) to find the invisible stalker then I would rule the Stalker uses a passive check (stealth) to be hidden, the result then would stealth 20.
Of note, the Invisible Stalker has no special Hide ability. However, it is always invisible, which means if it stays silent and doesn't leave tracks (signs of its passage) it gets the full benefit of the Invisibility condition, which is impossible to see.
The correct way to play a stalker (IMO) is
1. they are invisible and silent and thus hidden when PC enter their location, impossible to see. They have dark vision so they would prefer a dark or dim light room.
2. They will attempt to swoop in an attack, using stealth checks to stay silent on approach: "Stealth. Make a Dexterity (Stealth) check when you attempt to conceal yourself from enemies, slink past guards, slip away without being noticed, or sneak up on someone without being seen or heard."
3. When they attack they give away their position, so the PC can attempt an opportunity attack with disadvantage if the stalker moves away.
4. The stalker moves away to an unreachable position, once that limits line of sight, probably up or behind something to block attacks. The PCs would still know its location but might not be able to reach it or attack it with ranged weapons.
5. Stalker goes silent again, trying a stealth check, or swoops in to attack again.
The Stalker has several advantages that make it tough:
a. it almost always attacks with advantage (it always has the invisible condition) and has multiattack, so it will score many hits and many critical hits.
b. The stalker will almost always be attacked with disadvantage even if you know its location. The AC of 14 plays higher then it appears, as does its 104 HP.
c. it is intelligent and cunning (wis 15) so it knows that risking an opportunity attack is preferable to not moving and getting attacked multiple times.
d. it is intelligent and cunning (wis 15) so it knows to attack unarmored or weaker PCs first and has the movement to get there.
e. it is intelligent and cunning (wis 15) and knows that creatures that carry a light source probably need a light source so will attack the light source to put everyone in the dark. It will also understand the bright light and dim light effects, so it would retreat to the high dark corner of the room to get hidden.
f. It knows it has good strength so will try to use shove as appropriate to move weak PCs into hazards and off ledges.
g. it is intelligent and cunning (wis 15) so it would of course try things that don't break being hidden, say dumping burning oil from a chandelier or brazier over the PC's, forcing a save as opposed to attacking (and giving away its position)
h. It knows it can fly, so will choose areas to maximize its movement. It also knows if an enemy starts flying it is the most dangerous enemy.
They are tough enough.