EDIT: beaten to the punch by aaronjb There is a company near me that is able to repair those, costs about twice normal.
Because it's not legal
Hmmm, not the advice I was given. I believe it was vulcanised in accordance with the British Standard regulations at the time. It certainly allowed me to continue to use an almost brand new tyre until its normal wear limit. The puncture I had IIRC, was virtually identical to the one pictured.
Repairing outside of the Treaded area IS legal under BS AU 159(British Standard). HOWEVER, it is classified as a Major repair and not a Minor repair (the kind that can be glued and plugged). However, the big tyre sheds would prefer to use the words "can't" or "illegal" rather than admitting
they don't do it. After all, they aren't going to be able to sell you a new one if they do that are they?
The standard divides the tyre into areas T (treaded) and W(wall), and specifies the types of repairs that can be done in each area. Sadly I can't find a full text of the standard anywhere without paying for it, but there are places that will do it. It is worth noting that a Major repair will preclude any further repairs on the same tyre.
Whether you trust a tyre repaired in that way is a matter for the end user of course.