I know you say 'surely they'll miss the ongoing £30 from me not going anymore more than a one off £30' but you're misunderstanding I think.
When they implement a cancellation policy, across the board, they have no way of knowing whether charging someone (which the customer will have previously agreed to when signing up) will incentivise them to stop attending. Lots of people would just accept the charge as fair enough, you'll booked a slot you're not using and it's too short notice for them to fill it, and keep going. So by saying 'fine I won't go anymore' you'll be in the minority.
Additionally, having a robust cancellation policy is what protects their income. Otherwise every time someone cancels at 2pm for a 3pm appt and has their fee waived they've not only lost £30, they've also ensured that that customer will take that to be the policy and feel comfortable doing it again in the future. Losing many more £30s.
It's fairer to ALL to have a cancellation policy that applies regardless of personal circumstances. In very extreme situations they may choose to waive it (for example someone is due in Tuesday afternoon and finds out Tues morning their partner has died) but it probably comes out automatically anyway so you'd have to speak to someone to ask for it to be refunded/waived.
My piano teacher requires 24hr notice for cancellations/moving lessons, and if it's within 24hr they expect the payment for the lesson. Doesn't matter the reason, whether it's illness, work, whatever, it's fair to everyone and everyone knows the policy. Our swimming lessons are paid for whether the child attends or not because you've paid for a slot in that lesson, you can request to attend a catch up elsewhere in the week but they don't not charge you just because you can't make it. Once a piano teacher for example starts picking and choosing who to apply the lesson payment to when it comes to short notice cancellations it could easily lead to favouritism and discrimination.
No offence but everyone thinks their circumstance warrants special treatment. If you don't agree with their policy you shouldn't have signed up to them, and it's absolutely within your right to say now 'oh, this isn't the place for me'. But make sure you read the T&Cs of the next place.