Fine, an invisible potted plant.
An invisible potted plant doesn't need to use the stealth skill in order to be silent. Objects don't have skills; only creatures do.
For an invisible object in a room, the dungeon master simply sets a perception DC. Player characters might notice dead leaves from the potted plant, or the marks of it in the dirt.
An invisible creature sets its own perception DC.
Its stupid either way, no matter how hard you guys try to rules lawyer it.
It's not stupid. Again going back to your example of the invisible stalker, it has +10 to stealth. Odds are its going to generate at least a 20 on its stealth check, and if it's had sufficient time probably generate much more (It's been in the room long enough to probably get advantage on its stealth check, setting a passive perception DC of 25 to notice it).
Presuming a player character that entered the room has a passive perception of 25, he probably notices air swirling around suspiciously in the corner, and an ever so faint shimmering.The other player characters aren't going to notice it unless they spend their entire round taking the search action and crack a DC25 Perception check.
It almost certainly attacks with surprise, flies down and attacks a player character who is surprised, and then flies away (It is immune to attacks of opportunity remember) and then within a few seconds, the player characters again lose track of where it is (the following round it takes the hide action and rolls its stealth at +10).
Rinse and repeat.
If it was an invisible creature in full plate mail and with a dexterity of 8 on the other hand, Its skill is -1 and it rolls with disadvantage. You are hearing that clumsy fool in full plate from several metres away, and noticing his heavy boot prints leaving trails in the mud no worries at all.
But even the invisible idiot in full plate clanking like a small factory, is immune to Hex, Hold person, Hunters mark, Power word kill, Dominate person, Counterspell, Magic missile, Imprisonment, Haste, Harm... And the list goes on. Your vengeance paladin can't declare your third level Channel Divinity against him. You can't make attacks of opportunity at all against him either. Your attacks against him are all at disadvantage. His attacks at you are all at advantage. He can spend a few seconds when ever he wants to take the hide action, and if successful you can't attack him at all, and have to guess his location.
The only people who think it is stupid, don't understand the rule.