One hopeful tip : i had the exact same problem. Tried software reset, iOS update, physically bending(turns out table was bent. iPad was not). realized touch doesn’t work only when held in hands/moving/shaking. So disabled shake to undo which uses accelerometer and lock screen rotation. So far touch works flawless. Considering the problem appeared after iOS I-date, it definitely seems to be software problem that messes with the accelerometer. Might not work for everyone. But give it a try!
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