I think the issue with Psionics is, you can't design it for people who "don't want Psionics".
It's like, you can't design Artificers for people who are fundamentally against the idea (me according to some people lol!).
Equally, you can't design Fighters or Wizards for people who, fundamentally/conceptually don't like to play those things.
You have to design classes for the people who do like the basic concept.
The Mystic wasn't doomed by its design, it was doomed by requiring 70% approval in an environment when, well, probably less than 70% of people even want significant Psionics in D&D. As I've said many times, any Full Caster-type class, let alone with a new system, would be doomed if subjected to 70% approval. It's notable that Artificer wasn't subjected to the approval process (as in, there was no possibility of saying no to Artificers period), and frankly, even as a Half-Caster, it wouldn't have passed. I mean, can you imagine though, if 5E launched without Bards or Warlocks, and then tried to add them via the 70% approval process? There absolutely NO possibility either would have got through. It's harder to imagine re: Wizards/Clerics/Sorcerers, but if we imagine a D&D where Sorcerer was the main Arcane caster, and Wizard was added as an entirely new class, subject to the 70% approval, there's no way. People would just say it was a "boring and overpowered" version of the Sorcerer.
There's also just an absolute TON of stuff in fantasy literature which is called "magic" (or something that's not "magic" or "psionics" - it's pretty much never called that), but that in terms of what it does and how it works, is obviously much closer to Psionics than D&D's fire-and-forget-type magic. Good examples would be, like virtually all "Romantic Fantasy" (i.e. the stuff Blue Rose covers), which was historically a huge chunk of the market, where the good guys tend to use psychic powers and the badguys D&D-style magic, Robin Hobb's "Assassin" books (the entire setting there are what, like 19 books or something now?), where The Wit and The Skill are pretty much both forms of Psionics, tons of the modern equivalent of Romantic Fantasy, which is basically the (extremely successful and rarely discussed) "Teenage Assassin Girl" genre, and so on.
I will say that books where magic looks like Psionics are disproportionately written by female authors, and where magic looks like D&D-style magic disproportionately written by male authors, so I think there's a bit of sexism in the claims that "fantasy doesn't have psionics in it", and a bit of entirely-unconscious sexism in the opposition to psionics as part of D&D (i.e. "at all", rather than in a specific game).
I think if they'd just renamed it to something that wasn't psionics or psychic powers or the like we'd immediately see like a massive increase in its acceptance though.
This definitely fits the list for "didn't quite work", yeah.
The issue is that a lot of people don't want just a half-caster with a sword (available already as an Artificer Battle Smith), they want something like the Swordmage of 4E, where the magic is fully integrated into their combat, where they're not just sometimes casting spells. Or at least the Magus of PF2 (not PF1).
Bladesinging fits well for an OD&D/AD&D-style Gish i.e. "Fighter/Mage", but less well for what a lot of people want.