I'd rather all the money raised went on the food that people need rather than staff but maybe I'm just too naive.
You'd probably find that, over the course of 12 months, the cost of wasted food, downtime to vehicles etc woud be more than £35k if not properly organised.
I'll just use a small one as an example - the Stretford Foodbank is near to me (affiliated to Trussel) - they have collection points in the Asda, Sainsburys, so they need to organise collecting from there, then they need to get the stuff sorted, allocated and delivered (in unmarked vans). Someone has to manage all that, make sure the vans are road legal, volunteers are in and doing the jobs, recruiting volunteers and most importantly that the food is collected and distributed as soon as possible. No one person will volunteer for a role like that, so it needs a F/T staff member and its needs someone professional to do the job. If there were stories that the foodbank wasn't collecting, or worse, not delivering parcels, then the public could lose faith and stop donating to that particular bank.