Similar to fission products, neutron control material (like Boron) indeed does not absorb fast neutrons as much. Fortunately it still does absorb fast neutrons enough to control fast reactors (with which we have 430 reactor-years of experience or so).

Indeed fast reactors need higher fissile concentration to be critical. Some kinds of fast reactors (like the Bill Gates Traveling Wave Reactor idea, which, disclaimer: I have professional connections to) can breed up plutonium in spent fuel and then burn it down without reprocessing (to be fair, the spent fuel would have to be hot refabricated into metallic fuel first, but that's still not separations/reprocessing). This kind of reactor needs enrichment once (to start up) and then can just be fed natural, DU, or SNF and it will run on a stream of it happily "forever" (until the vessel life is reached, at which point you transfer the core to a new machine and keep on shuffling). Only fast neutron systems can do such a thing. The Fast Mixed-Spectrum Reactor idea of BNL in 1980 was similar. Many fast-neutron MSRs are the same.

Fast fission is not all that's at play in a fast reactor. It's all about Eta (neutrons released vs. neutrons absorbed in fuel). In a fast reactor, it skyrockets around 0.5 - 1 MeV because of three different physical facts: neutrons released per fission goes up with fast incident neutrons, fission cross section stays flat for all actinides around this range, and capture cross sections drop off towards zero around this range. This is discussed on: https://whatisnuclear.com/fast-reactor.html#havingmore

Having extra neutrons around means you can afford to invest more in breeding fissile material, and only fast neutrons can get you to the point where reactivity is flat or increasing instead of decreasing as fission products are produced. The only exception is Thorium fuel cycle, where U-233 releases a lot of neutrons even with thermal neutron absorption. In that case you have to be removing the fission products as they are created with separations, and this basically is only practical with fluid fuel. This was the idea of the Molten Salt Breeder Reactor project of Oak Ridge in the late 1960s.

With reprocessing, you can definitely re-concentrate the remaining fissile material and get a thermal reactor critical again to burn it. But you cannot meaningfully use the other actinides as fuel, which is the whole idea of "running on spent fuel".

Regarding that slide deck, I love the idea of molten fuel in tubes. I investigated it heavily once upon a time, being super excited about it. I ran into the problem that while salt fuel mass densities are low, separating them out even more physically makes the fissile density annoyingly low, to the point that I couldn't get the reactor performance I wanted for my then target market. I still think this concept is very interesting so I hope these folks do well. They won't be extracting any non-fissile energy from SNF though until they replace that moderating fluid with something like lead, gas, or sodium and change their fuel salt to a chloride.

CANDUs can't use straight-up SNF out of a LWR without first stripping out the fission products. They're an example of "burning down the fissile material even better" but not "extracting the 100x more energy from the fertile U238".

BTW the safety example in that slide deck is a bit disingenuous by suggesting that traditional reactors are not physically stable. If you know those guys you might want to tell them. Overmoderation and Doppler and the NRC ensure that they are inherently stable at power. These things aren't like the F-22 or whatever, requiring active systems to stay in the air. The engineered safety systems are simply for removing decay heat, which can be done passively in Gen III+ plants and indefinitely in any Gen-IV plant.