I had a mine surgically removed when i was around 30, bottom 2 were impacted with hooked roots like rivets, was on NHS list for years to get them removed, my private cover refused to touch them, then one of them shattered, and got infected so private all of a sudden said they would pay, day of the op was when I popped positive for diabetes, so surgery got cancelled for 6 months till my sugars were under control, (was lucky by all accounts my cousins diabetes arrived at the same age and he found out when he woke up in hospital).
Finally hacked out my bad rotten tooth after a 3+ year saga and was sooo rotten that I got permanent nerve damage in my jaw, so now bottom jaw left side is numb and front left tip of my tounge. and im missing a chunk of jaw hey had to hack out as well, Airports always think i have something in my mouth.
Private Insurance also said after the surgery that they would only pay for 1 of the 4 teeth they removed, so that turned into a bunch of drama as well, but to be fair to the surgeon he sorted most of that out, and I never had to pay anything in the end.