In defence of clubs in general...
Most clubs that I know have no or virtually no paid staff. All work is done by volunteers. The treasurer may not be a career treasurer, may not have a treasurers education, and the contracts/facilities with their bank account may be limited, either because they tried to obtain the cheapest service from the bank, or because of the limited treasurers knowledge.
Also, different forms of payment require different ways of keeping records and one method may involve more steps and people than another.
Furthermore, most clubs live in shacks at airfields where it's not a good idea to keep large amounts of cash overnight. So all the cash has to be taken home, or deposited in the bank each day. And even then, cash is almost impossible to insure.
All of this may lead to a preferred method of payment of your annual membership fee, with either an incentive (discount) for paying in the correct fashion, or a punishment (uplift) for paying in a non-preferred way. I don't think it's entirely fair to call that punishment the "administration fee" since the volunteer works for free, but I can understand that that term causes the least amount of discussion.
From my personal experience as volunteer treasurer (in several non-aviation related clubs), a direct debit mandate (or whatever that's called in the UK) is by far the easiest method of payment. Sure, as the treasurer you've got to input the direct debit mandate details into the computer once, but from that point on you can process 100s of invoices in literally a second. And I don't know how things work in the UK, but in the Netherlands you are only required to keep the signed mandate on file, but you don't have to present these signed mandates to your bank beforehand. Furthermore, it's impossible for the invoiced people to forget or "forget" to pay the invoice. The only remaining problem is a few (typically less than 1%, if you do things right) people who phone their bank claiming the transaction was improper, so it's rolled back. So for ease of use, a direct debit mandate is the best option for invoicing anything, from the treasurers point of view.
Cash, on the other hand, is the worst option. The trouble with cash, in addition to miscalculation/theft issues, is that it doesn't *automatically* generate an audit trail, like a direct debit mandate, or a credit card/debit card payment, or a bank transfer does. So there is extra work in creating this audit trail. And obviously, without a proper audit trail your administration breaks down, and there is an opportunity for dishonest people to skim off cash without anybody knowing what happened.
In the clubs I was treasurer for, I completely abolished the use of cash. Which made things really easy since *all* transactions were done via a single bank account, so the bank statements were all I needed to keep as underlying records for my ledger. But these were the types of clubs where this was possible, fortunately, and I appreciate that not all clubs are able to abolish cash altogether.
If I were a member at this club, I would be very inclined to recoup my 10% by way of stirring up a lot of feeling against this dubious practise and doing what I could to get the person(s) who thought this one up removed from the committee.
Noah, I challenge you to become a volunteer treasurer for a medium-sized club of any sort (say along the lines of 100-300 members) for a year or three, and then see if you still support that statement you just made.
Being a treasurer, volunteer or paid, is not a high-glamour job. You never get a compliment if your books are in order. Instead, you get to deal with the **** (insert your favourite synonym for excrement here) if people refuse payment for some reason or another. If you make a mistake, the whole club suffers. And even if everything is going smoothly, it's a heck of a lot of work, at least a few hours every week. Which, obviously, nobody notices.
And if you then have a few people at the annual club meeting who start "stirring up a lot of feeling" with the aim to "remove you from the committee", the fun of being the treasurer wears off rather quickly.
I once heard an analogy which sums up the situation rather well, IMHO. In every club, there's 10% people who are pulling the cart forwards, 80% people who are sitting in the cart along for the ride, and 10% trying to pull the cart back. In which group are you?