the CSD came and looked at the situation and filled out a defect log herself
she would be writing a strong letter to Customer services
Seems to me she did both.
But you, Sir, the OP, are amazingly tolerant! You had what seems to have been an unsafe seat, and certainly a very uncomfortable ride. It's worth a hell of a lot more than an emollient email and £30.
Personally, I would have refused to even sit in the seat, on safety grounds as well as comfort and contractual grounds, and let them sort out whether to offer an upgrade (the obvious choice if available) or offload, compensation, 4* hotac, a seat on their next available service (with upgrade if necessary) within 24 hours or a transfer to another carrier, the whole 9 yards.
So the answer to your question is that your seat seems to have been way over the threshold for
proper compensation!
Airlines should NOT be allowed to get away with this kind of crap; the cabin staff should have offered all the above, not tried to fob you off. Above all, the aircraft should not have been given a CRS (ie released for service) with a seat in that condition, unless it was tagged as u/s and unfit for service. If they behave this way with visible defects, imagine what might go on with the others.
If you have the time and inclination, and do not get a positive and rapid response from the airline, consider writing with the facts to their regulatory authority. And there's no harm in naming them in this forum so long as the facts are clear and true. I know there's a clue in your post, but it's a bit obscure.
By the way I had exactly the same problem on BA BOM/LHR a fears years ago; I did refuse the seat, so the cabin crew promptly upgraded an ID90 staff traveller (fellow cabin crew) and gave me her economy seat! That's just BA's little way; I had no cause for complaint.