Braids, Cabal Minion did not make a big splash when it was in Standard – the only reference I could find was John Larkin’s UB Braids rogue deck. Today, Braids is a serious combo with things like Awakening Zone and Mogg War Marshal. The abundance of tokens in modern Magic made it a much stronger than it used to be.
I don’t run Stax as an archetype in the Elegant Cube. Although it sounds unfun, I don’t see much hate against it like against land destruction, counterspells, or uh… Lantern Control. The deck needs to close the game at some point and usually sees no resistance, so the game doesn’t usually drag for too long. It’s a fast concede/loss, unlike the other decks mentioned above.
Stax is a pretty unique type of deck in cube. Most other prison decks are highly siloed, but Stax doesn’t need to be built out of very specific pieces, so it takes up few slots and doesn’t warp the pool. Other cards that compose the archetype are Smallpox, Deathcloud and Tangle Wire (this last one much more polarizing).
I used to run Smokestack, which along with Braids is probably enough for the archetype to exist, making it pretty space-efficient, but no one in my group seems to like the sort of deck, so I moved the artifact to Occasionals, and left Braids as a simple, easier to interact version of the effect, which acts as sacrifice enabler and payoff. Smokestack in Occasionals makes the stax deck available occasionally, since Braids will likely be in the draft too.
Gameplay-wise, Braids seems much more risky to use than it actually is. You can sacrifice her to herself, so the baseline is making the opponent sacrifice a permanent and maybe chump one of their blocks.
What I don’t like
The role of Braids in the Elegant Cube is a bit narrow. It is very good in the sacrifice deck, and fine with any sort of tokens, but other decks rarely want to run it.
Desolate Lighthouse - MTG Cube Theory 