[RPG] Does a ranged attack around a corner incur cover penalties

In the first case, it is clear that the attacker has line of sight. The attacker is totally unobstructed from the target.

In the second case, the attacker does not have line of sight, and cannot attack the target with a sight-dependent attack. The attacker could, however, move to the side, which would allow them to attack the target (whou would have cover).

In the third case, there is line of sight, as the attacker can see the target's square. The target does, however, have cover:

To determine whether your target has cover from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target’s square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the target has cover (+4 to AC). — d20 SRD, "Cover"

I've made a helpful diagram (code) to detail what's happening:

The red lines detail corners which cross through walls. The blue lines detail corners which are questionable at best. The green lines indicate that there is, indeed, line of sight.

The green line from the bottom right of the attacker's square to the top left of the target's square passes through the gap between the spaces; ergo, there is a line of sight. However, every other pair of lines passes through (red) or next to (blue) one wall; ergo, the target has cover.

This is absolutely counter-intuitive for me, when you mechanically can't effectively hide behind a 5 foot tree against a non-moving attacker.

What you need to understand is that the mechanics of combat are intended to function as abstractions for what actually happens in combat. Diegetically, the combatants aren't literally standing in place, waiting for all the other combatants to finish their "turn", every six seconds. That's just an abstraction we use to keep combat tactical and strategic.

Or, put another way: if you're a creature that is benefitting from half-cover, the only way you can then make an attack is if you physically move out of the way of that cover. It may not require you to use up movement speed (if, for example, you're peeking around the corner) but regardless, it's not like a potential assailant would specifically wait for you to make your attack and then retreat before trying to make their own attack; in fact, they'd probably specifically use the moment when you pop out of cover to make their attack.

^{Just to be clear, I'm not talking in terms of game mechanics; under most conditions, it's not possible for a creature to make an attack during someone else's turn, without using their Reaction or some other clearly specified game mechanic. I'm purely talking in terms of Narrative Diegesis, where "turns" don't exist and everything that characters do in combat is happening (relatively) simultaneously.}

But of course that makes it more difficult, hence the mechanical advantage granted by cover of having extra AC, making it harder to successfully land a shot. In this context, the +2AC granted by half-cover is the abstraction meant to explain the difficulty of timing a shot to line up with when you pop out of cover.

This also holds for other kinds of cover: Half Cover abstracts for the fact that, due to being just half cover, maybe part of your body is sticking out beyond the cover outside of your control, whereas with 3/4ths cover, maybe this is no longer an issue. Narratively, how you justify these abstractions is ultimately down to the DM, or for flavor purposes, the players themselves.

So it might seem weird that a 5-ft tree is unable to completely block incoming attacks from hostile creatures, but once you follow how combat is abstracted around cover and the use of obstacles in turn-based combat, I think it's more understandable why these mechanics work the way they do.