EASA put it so much better than the rest of us. For commercial air transport at least (and you'd think the guidance would be sensible across all forms of flying):
https://www.caa.co.uk/docs/33/Inform...ice2014022.pdf
The operator shall not permit any person to use a portable electronic device (PED) on board an aircraft that could adversely affect the performance of the aircraft’s systems and equipment, and shall take all reasonable measures to prevent such use.
This means that there is per se no ban on the use of PEDs. However, the operator is required to demonstrate that radio frequency emissions from PEDs do not pose a risk to aircraft systems and equipment and that all hazards are mitigated before allowing the use of PEDs on board.
They are, I should point out, specifically talking about non-transmitting PEDs, where less stringent rules apply. If the operator had carried out a demonstration similar to that highlighted in bold and proven that texts could not have an adverse effect on aircraft systems, at least the only question that remains is the issue of distraction from the primary flying task.