@IC quote "To save others the trouble... Discussion: Why don't aircraft weight themselves?"
...and fly themselves? That's coming too.
Mistakes happen, it's the crews who catch them before the bad consequences that keep us safe. If the airplane had its own scales in the gear, that might be a truly good cross-check, but if it becomes the primary means of establishing the GWT, the crew's mental cross-check is likely to vanish.
Failures occur in any electro-mechanical system, and I doubt the automatic system would have the integrity/redundancy to be the primary means. But it would no doubt be used that way.