You're completely correct
And the most galling thing about the entire affair is that it's still called 'insurance', rather than a more appropriate name: 'tax' or, potentially, 'credit agreement'.
As you point out, the idea is that you pay a small amount on a regular basis such that should a rare and infrequent incident occur, your costs are covered. This, in my mind, is how insurance SHOULD work.
If you pay the small fee, have an incident, then have to pay an excess, and then the 'insurance' company pays out the remaining costs, only to recoup those costs from you the next year by putting up your premiums - even if it was a non-fault accident in some cases! - then this isn't insurance. This is a credit agreement - deferred payment.
This, of course, forgets the fact that the 'insurance' company has already profited greatly from you for the long years between incidents, assuming one has ever occurred at all.
My mind is drawn to similarities to the TV License, or the BBC Tax as I think of it. It is there to, theoretically, fund the BBC (TV, radio, et al). And yet, you are given no option to NOT pay it, even if you do not wish to partake of the Beeb.