There are two separate issues raised here.

Firstly, a 'not for profit' organisation is not prohibited from making a profit - what it means is that any operational surplus is ploughed back into achieving its objectives rather than distributed to shareholders as dividends. NPOs are't prohibited from dealing with profit-making organisations, and if they were it would be impossible for them to operate - how could they purchase anything from stationery to biscuits or get legal or accounting advice? They are allowed to operate in the real world.

Someone organising an event has the choice between handling ticket sales themselves or contracting it to a third party. Many organisations don't have the resources to have someone on standby to handle ticket sales, and if they can only be sold during someone's spare time they are likely to lose sales. An agency can advertise more widely and and operate in normal working hours, and if they are online provide a 24 hour service. However they are businesses and expect to get paid for the service they provide.

When you buy a ticket direct from the promoter or the venue the handling costs are hidden in the price. The objection to these agencies appears to be that the costs are added on during the booking process so the final cost is more than expected. However the real question is whether the concert is value for money. Would it have made a difference to you if the tickets had been advertised at the final price in the first place?

Not a fraud, but a charge for providing a service. Unfortunately not all ticket sellers follow best practice. All the charges must be stated but if these are hidden away in the T&Cs then they're easy to miss. However these charges are well-known and it shouldn't really come as a surprise that they're added.

A promoter has to balance the risk that the charges will put some people off against the hope that a ticket seller will provide a more effective service and will achieve more sales than doing it themselves.