I think the answer depends upon your council's particular circumstances. If you have the facility to print documents then absolutely documents should be provided in paper form if requested to do so.
Whilst the allowance is intended to cover the additional costs of being a councillor, few councils actually pay an allowance and I believe co-opted councillors cannot claim it. Where it is paid, I would expect the costs associated with printing papers for meeting to be covered through the allowance.
Councils can provide whatever equipment they feel appropriate to enable members to undertake their role. These days many councils provide a tablet or laptop (mine don't!) so I presume a printer would fall into that category of appropriate equipment albeit I personally think it's a bit excessive. Of course, if a printer is provided, I wouldn't also be expecting the clerk to produce paper copies for those members for the meeting.
I personally prefer a paper copy at the meeting as it's easier to refer to during proceedings. I print my own, and don't expect to be reimbursed the cost. My council does provide paper copies, if requested. I do see other councillors pick up copies intended for the public in the meeting room.