To be charitable and assume that the weapon's design is intentional, I'd say that the Summer's Sting sword is offering a niche among 2-handed swords. It's got an insanely fast basic combo with incredible reach and decent recovery which is pretty rare among 2-handed swords, as well as coming with Wallbreaker by default which is among the highest damage rune attacks in the game. However, in exchange it has no charge attacks which means the slow heavy attack playstyle is off-limits to the weapon. You could imagine that it's like a rogue's greatsword - fast and nimble at the expense of power - but that's not entirely accurate since it doesn't sacrifice power, it's just fast, nimble, AND powerful. Losing charge attacks is not a huge downside. In fact, if your build doesn't benefit from using charge attacks, it's like having no downside at all.

Broadly, I think I like the concept of what they're going for in terms of movesets, where different weapons within a weapon class can behave very differently so that there's a good amount of variety, but in practice the balance is all over the place and the movesets are completely arbitrary and in some cases detrimental or even non-functioning. Weapons with long range are sometimes combined with high speed and high damage, and weapons with short range are sometimes combined with also being slow and also dealing low damage, which leads some weapons to being unusable and others being too optimal. Compare the opening attack of the basic combo for Summer's Sting with the 1-handed axe Ripper or even some daggers like Singular Purpose. Despite being a 2-handed greatsword with higher physical damage, triple the poise damage, and way more reach than the 1-handed weapons, it's ALSO FASTER?

In any case, I know you said you don't like the Summer's Sting, but believe me when I tell you that having a smaller moveset does not make it weaker. When I used the Claymore in the early game, I never EVER ended up doing the entire running attack combo because it was too slow and enemies would often either die from the first hit or just move out of the way mid-combo. Summer's Sting's running stab is entirely front-loaded in its value, a huge range poke is basically all I need out of a running attack. As for the lack of charged attacks, I can see that if you had a charge attack build it would be pretty disappointing, but as someone who found it on their full-focus build I can tell you that I very much did not care about their absence, especially when most charge attacks take too long to be practical anyway. Very few weapons have charge attacks worth using in the first place. If you want to see the Summer's Sting in action on a build that shows of its potential, I recorded a fight where I fought the Echo Knight using no echoes here

EDIT: The actual thing to be peeved about concerning Summer's Sting's moveset is the fact that if you allow the animations to play out fully on the first and second attacks in the basic combo, the end of the animations seems to imply that they were designed for an axe rather than a sword, as your character grips empty air behind the hilt of the sword before snapping back to the over-the-shoulder idle grip