It is not just a phone call - if you want to change your booking there are fees and fare differentials to be paid for so a third party (the handling agent) can not do this on the passenger's behalf.
You might be able to it by mobile from airside if the agent has the facility to access the departure control system from airside and amend the two sets of flight details and print a new boarding card. It is not normal for this to be available airside for EZY as this facility carries and additional cost on every departure to the carrier and is utilised very rarely.
EZY do not pay their airport handling agents to provide any more than a very basic service; this does not include airside ticketing services nor providing 'runners' to provide the service in the event of a delay.
Sadly, long gone are the days when this could be done quickly and manually; the low cost carriers all have sophisticated fare yield programmes and your wife would probably have got an horrible shock at the cost of a ticket bought only a very short time before departure.
As the man said, you pay your money and take your choice.