BALPA are not powerless, just not omnipotent as some would like.
For the last time you don’t pay 1%...its tax deductable therefore the taxman gives it back as a tax allowance. I can’t say it any clearer than that.
There is only any value at all, if they can and will fight the corner, surely? Otherwise, as others have mentioned you're better off saving your 1% per month and putting into a sinking fund for your own protection, perhaps organising some kind of co-operative agreement with fellow pilots that you'll support each other if the fees exceed what you've squirrelled?
Trust me, BALPA find it hard enough to keep the workforce onside when things go pear shaped. Good luck to you all if you honestly believe your colleagues will stand by you with cash in hand, ready to help you out when the time comes.