As others have stated, retreading is alive and well. It is mainly used in situations where it makes sense economically - trucks, aircraft, that sort of thing.
But for smaller tires, it just doesn’t make sense to retread a tire when a new one is only a few dollars more.
Truck and aircraft tires have been designed to be retreaded, car and light truck tires have not. That means the retreader is taking a risk on car and LT tires that he isn’t with truck and aircraft tires.
Also, there are 2 types of retreads - cap and full. In the case of a full retread, and the tread and the sidewall are replaced to the point where the original tire brand may be obscured.
The cap - commonly called recap - is just replacing the tread. In that case, you can still read the name of the original tire manufacturer.
The most common cap is for the tread to be made (and cured) as a separate unit and cut to length with a bonding layer of rubber between the precured tread and the casing. Not only can the tread be made of rubber that will wear better than can be processed the other way (by extrusion), the process makes for very dense rubber.
Oh, and regrooving? Perfectly acceptable on tires that are regrooveable - it will say so on the sidewall. But you do have to do it in a way that makes sense. And “X” pattern is not that way.
And lastly: BillRussell said: “I was driving on Rt 95 one day, in the left land, and saw what appeared to be a tire rolling down the highway next to a car in the far right lane. Both moved into the breakdown lane. Later I realized what I saw was the tread that had totally separated from the tire in one piece and was rolling down the road. It was either a bad retread, or a badly manufactured tire.”
That was most likely a Runflat - a tire operated without benefit of inflation pressure and damaged to the point where the sidewalls detach from the tread, leaving the tread as a hoop. If you had captured that hoop, there is a 90% probability you could have found the hole that let the air out. The other 10%? The hole is in the damaged area and can’t be located because of the damage.