There's a big difference between "it's possible" and "it will happen". I mean, look at air travel for example. Supersonic air travel has been possible since the '70s. But it doesn't happen because it's not cost effective, and the benefit from it never outweighed the cost.
I think it's possible that we can to send a human consciousness (physical astronaut, uploaded mind, etc.) to Proxima Centauri in a thousand years. But will we? "It would be amazing", as it turns out, isn't actually a very strong justification for doing anything.
Doesn't happen now, because the sole craft was eventually retired. (Rather spitefully, too, with BA refusing to cede any to Virgin)
There is, nonetheless, Skylon under development, though dreadfully underfunded. If it actually works as expected, SABRE will be a quite remarkable innovation. So far, it's all looking good, including the particularly gnarly issue of cooling the incoming air in extremely little time.
I think it's possible that we can to send a human consciousness (physical astronaut, uploaded mind, etc.) to Proxima Centauri in a thousand years. But will we? "It would be amazing", as it turns out, isn't actually a very strong justification for doing anything.