Psionics has traditionally all about providing players with boatloads of advantage and xxxploitz to bring to the table and make the DM cry. And 5e rewrite of the psionicist would have to stick to tradition on these important points.
Even before there was a dedicated psychic class, even in OD&D and in 1st edition, the idea was that you get better and better with your powers, as opposed to having higher and higher level spells. Because it's something that you do. Like a skill. As opposed to magic, which is something that you use.
That's what makes psionics psionics. Even the concept of psionics strength points is based on that narrative feature. Spell slots are these abstract receptacles for these alien magical-mental entities, which is not applicable to psionics. Because psionics is just something that you do.
I totally believe you that your pessimism is historically justified, but when I look at the way 5E manages to build classes, and when I look at 5E in general, there's this incredible flexibility in the system that can very nicely combine different kinds of character progression. Of course a purely skill-like character progression would be very difficult to make balanced. But I think that 5E can be able to push this skill-like concept of level-of-mastery that defines psionics, it can push it really far, because it can nicely surround it with supporting class features.
I agree with Gargoyle, WotC should really take their time with it.
The situation that you're referring to, when the player picks a psionicist from the rulebook and drops it in the DM's non-psionic campaign, I think that maybe 5E can make even that work.
Although to be honest, I'm not really worried about that. That's an extreme scenario. A psionicist PC class should be something that the DM's campaign provides as an option. And not something that the PC brings to the table and shoves it into a classical campaign.
What I'm more interested in is Dark Sun. It would be nice to have a wild talent feat, because Dark Sun is not Dark Sun without that. In Dark Sun psionics is much more prevalent than magic. So the issues are very different from the plug-and-play psychic scenario.