I've since become head of technology at my office, and years ago we've had a policy in place by my boss which was not to directly take phones away, but to heavily discourage their use in various fashions. (Which some people ignored anyway).
I successfully argued a case against that and got the policy reversed.
Several of the departments, especially ones primarily staffed by people my age and younger, saw some definitive productivity increases almost immediately thereafter. Many use the phones for spotify and other music services. I know one guy uses it to listen to financial podcasts so he can do his job better. Several others use it to complement the security policy by having a keepass database on them at all times.
Not everyone is productive in the same manner.
If I was OP, I'd go to whomever makes the policies or advises on technology and ask them to fight it, because I can legit see how not having a little music or other productivity aid can actually hurt your output in the end.