> But breeders themselves are uncompetitive
Hard to say. Hasn't really been commercialized to the point one could make any definite conclusion. There's nothing inherent in a breeder reactor that would make it substantially more expensive.
> and fast breeders are inherently dangerous, since they require much higher concentrations of fissionable material, and could potentially experience fast prompt supercriticality in severe accidents.)
No. In a fast reactor the prompt neutron multiplication time is an order or magnitude faster than in a thermal reactor, but still several orders of magnitude slower than in a weapon. Further, the enrichment is much lower than in a weapon (recent-ish designs are made to work below the 20% HEU limit for obvious reasons), so it's quite unclear if it's even possible to get all the material into a suitable geometry before it would blow itself apart.
Of course it's possible to have a criticality excursion that would destroy the reactor, but those are possible in thermal reactors as well.
> If nuclear is not competitive with cheap uranium and burner reactors, it's not going to be competitive with breeders and reprocessing.
The fuel cycle costs are basically fuel + enrichment + disposal for a once-through thermal cycle, and fuel + reprocessing + disposal for the breeding cycle. Fuel and disposal costs would be lower for the breeding cycle, although with current prices and maturity level of the technology you're correct that the once-through cycle is cheaper. Not written in the stars that it will remain so forevermore, though, and breeder + reprocessing tech is waiting in the drawer for that day, in case there ever will be a need. No hurry.