Breeders could fix that, but haven't they been disastrous so far?

I'm under the impression that the reasons why breeders haven't been taken into use are almost completely political. I can't claim any deep knowledge of this subject, but it seems that there are some extremely promising designs in existence. One example is the Integral Fast Reactor.

If the IFR and other advanced reactor designs are as great as they seem to be, why are we worrying about peak oil? And why spend massive resources on fusion research if breeder designs could be finished with relatively little effort?

Breeders are more expensive to build and harder to maintain since it is fairly easy to maintain water filled equipment but much harder with equipment full of molten metal or salt. Molten metals and salts are not transparent making inspection much harder and they are not liquid at room temperature.  You can for instance easily use acids to etch away the irradiated surface inside a water based reactor vessel and then go down and make manual repairs inside a reactor vessel that has been in use for 20 years.

Breeders do not make economical sense when nuclear fuel is cheap.

But imagine if coal power worked like nuclear power. When coal get scarse you dig up the ash, put it in a twise as expensive powerplant and get at least  ten times the energy you got the first time you burnt the coal.

Spending lots of money on fusion research makes sense for me, plasma physics and extreme materials will likely have other uses and if we get fusion to work in an economical way we have another exelent energy source.  What is dumd is to not also spend research money on better fission technology, your example of one such promising technology is very good.

All kinds of energy production and efficiency in energy use needs to researched and developed in parallell.

Actually the reasons are both political and economical.
In recent years (before 2004) price of uranium was well below 12$/lb. This was mainly due to Russia flooding the market with fuel from decomissioned nuclear weapons.
With the surge of oil and NG prices the uranium price also rose to 22$/lb now and predictably is set to rise. At some point breeders will become economically feasible. Anyway this is the future because something must replace fossil fuels and this will no way be renewables only. IMO we will sooner or later get there but probably a major crisis should happen first.
Gas cooled fast reactors work very well, but the political support is for liquid metal cooled reactors because the existing companies have invested in the technology and won't gain if we switch emphasis.