Yes it does happen. Yes they do get reported. Yes, if there is merit the insurers ( as in most such cases) will try and limit the damages costs etc.,etc by settling. Some cases do not have any merit. There was a case last year where ( I think) beneficiaries sought to sue a solicitor involved in a probate case - there were quite scurrilous accusations made against the solicitors who rightly defended the case and did not settle.
The Law Society has a panel of solicitors who will act in negligence actions against other solicitors. I do it and regularly receive calls from people who want to take negligence actions. But I am also shocked at the number of people who contact me to make complaints about solicitors when there is very little merit in their complaint and who are simply unhappy with their situation.
We don't have magic wands and there is no magic pot of gold to dig people out of unfortunate circumstances. And I do accept that some solicitors do seriously let their clients down. It will always happen in any profession - we (lawyers) should always try to limit those situations. So should doctors , accountants, dentists etc.,etc.
mf