Why aren't all strongly self-recognizing T cells made into regulatory T cells?
The selection is based upon the strength of the binding. A strong bond causes a signal in the T-cell to self destruct (apoptosis).

Wikipedia has a post on T cells. Perhaps the moderate bonding become regulatory cells, because these cells have to recognize those T cells that survive negative selection, which are most likely to cause autoimmune responses over a long period of time. 

Strong affinity to self means the immune response will become a danger to the host.