I think I will talk to my DM about Heavily Obscured and Full Cover. If they cannot see or target you, you should be able to hide ... I am totally fine with a PC re-hiding as long as it makes sense.
They CAN hide whenever opponent's cannot see them, but as soon as they move (to be able to attack the enemy) they lose their hiding place. So whats the point?
The concept that one needs to be some special race or have a special feat in order to hide mid-combat seems strange in D&D. Not that it should be easy to hide in combat, it should not. Only in perfect storm situations (like the one with the Desk and other furniture around) should there even be a chance.
You can hide when you have 100% coverage... but then you can't attack, unless they come to you. So you cannot use this to hide/attack/hide/attack "in combat". The special race and the skulker feat CREATE the scenario where YOU only need light obscurement (shadows, mist, a desk) to hide, and you can STILL SEE your opponent, so you can still attack them.
And this solves the Lightfoot Halfling thing too (at least in my mind) which there were several threads on. He cannot just re-hide in combat behind a larger PC unless the DM rules that he can (typically first round before foes know where he is). Once he attacks, everyone knows where he is. But there will be times in combat when he can re-hide, but they would tend to be rare. He would need to be totally unseen again (go invisible, go behind total cover, etc.) in order to hide again.
The lightfoot halfling can SPECIFICALLY hide right there in combat, with only the coverage from another person. But i agree that the enemy 'still knows hes there' they just cannot detect him, giving him Advantage on his attacks. But they'd certainly prioritize the pair of them with a fireball.
(typically first round before foes know where he is)
This is the conditions for every normal PC to be in stealth in every normal situation. By your example the Lightfoot Halfling would have no benefit.
If a PC can be totally unseen and unheard in combat, then it resets the clock so to speak. He goes behind total cover and then goes into lightly obscured and hides, the NPC that goes looking for him still needs to find him because he re-hid out of sight of the NPC.
I totally agree, he's found a 'hiding spot' but this doesn't let him ATTACK every turn with Advantage, because he cannot leave total cover without exposing himself (without the Skulker perk). Imagine round after round, the rogue comes from behind the total cover, fires at you, and returns behind his total cover (and hides). Can you attack him? No. Is he in total cover? Yes. Is he hiding? Yep, so even if I ran over there, he can elude me if he's very stealthy.
However, on each of the rogue's attacks, when he comes back out from behind the desk and fires at me, are you 'surprised' ? Are you being 'attacked by an unseens attacker?' Is the rogue 'in his hiding place?' No. So effectively, total cover lets you HIDE, and it's 'in combat' but this is not at all what I was discussing when I say "Hide In Combat" I'm talking about effectively Hiding + Firing + Hiding + Firing, to gain Advantage from stealth.
This requires a Lightfoot Halfling, a Wood elf in mist, or Skulker "the perk that lets you do it". Even with these things, you need SOME qualification (light obscurement) for instance, it needs to be dark. In a dark room in a dungeon, or behind some furniture, the Skulker has no obscurement. On a bright beach in the sun, the Skulker has no obscurement.
The Lightfoot Halfling can ALWAYS hide behind his buddy though, even in broad daylight.