Sibling comments are correct that weighted keys, graded hammer action, etc are all much better than a plastic level but still don't have a proper sense of touch that is linked directly to the sound.
It's not even a matter of training with a particular touch and being used to it - the link between the body and the sound is incredibly important and mechanical means of making the link are still far superior.
Regardless of what pianists will tell you, there is just one variable (hammer velocity) to actual sound production (by that point the hammer is decoupled from the key and whatever you do to the key after the first 5-7 mm of travel is of no consequence).
So the only "real" problem to solve is correctly measuring the desired speed and launching the hammer quickly enough.
While it may be true that velocity is the only variable, it's not a physics problem. As a player you can't choose the instantaneous velocity for the note, and the note is played at the same time or immediately before/after other notes, which all adds more variables to the touch and the movement of the musician.
Therefore the whole action matters, including how the key travels, the decoupling point, the resistance of the multiple parts of the action, the rebound... etc
It's interesting you're happy to disregard pianists opinions on the matter. Perhaps you think experts are too mired in tradition to see the truth? That may be true sometimes, but you also don't have the same grasp of what's involved as they do.
I know for a fact that experts can't tell Stradivari from modern high quality violins, can't tell if two glasses of wine are from across the world of each other or from the same bottle, rumours are they can't tell whether they're listening to a recording or live string quartet.
https://www.science.org/content/article/million-dollar-strad...
https://www.theguardian.com/lifeandstyle/2013/jun/23/wine-ta...
There is quite some variation between real piano actions of grand vs upright, 18th century and modern, German vs French vs English action etc. There's also no magic about either of them and no fundamental reason why an electronically coupled action couldn't exactly mimic them.
I don't see how that or a blind test is relevant to what I wrote anyway? Except for a cheap dismissal.
All I want to say is human perception is crap. You often think you feel something but you don't, you project your biases and external suggestions onto your senses and end up with yesterday's weather on Mars.
Therefore the most logical way to test whether you can really sense the difference is to deprive you of any reference for your biases, the double blind test.
> Electronic keyboards have weighted keys and similar tactile feedback to regular acoustic pianos, so this is a solved problem.
For professionals, the difference is huge. Seriously massive, on even the most expensive electronic keyboards. This is why I replied (unusual for me) - saying "it's a solved problem" is so far off the mark
Not to any rigid standard, but some pro musicians can't tell the difference it seems.