RE "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)"
As fission product concentration increases, even fast reactors have to remove fuel and reprocess it. What works for boron also works for fission products. I don't think any reactor (fast or thermal) can close fuel cycle without the help of reprocessing. May be fast reactors need less frequent reprocessing, that's it.

(LWR-SNF cannot go fast critical. May be fission products is not removed, but reprocessing is needed to concentrate Pu in LWR-SNF.)
Even if LWR-SNF has to be used as-is, it has to be toasted in blanket region of fast reactor before it is used as fuel. Some designs like TWR claim no reprocessing needed between toast step and burn step. I agree with that. But, for complete fission of SNF, fission-product removal is needed at some stage when fission product concentration exceeds a particular level in the fuel rod. No exception for travelling wave burnup.

For a critical reactor core some minimum length of fuel rod is always required to be in use. If fission product starts accumulating from bottom of the fuel-rod towards top, somewhere at the midway core can't go critical because a minimum length of rod is needed for criticality.

4% of 1GW-LWR fuel runs for 4.5 years. 100% of this fuel has potential for 112.5 years. A solid-fuel rod can't maintain integrity for 100 years. The crystal structure damage can't be reversed by any amount of maintenance. This is the same phenomenon how solar panels get degraded in sunlight.
A fuel rod has crystal structure damage by radiation as well as by fission products.

Fluid-fuel can be used indefinite time and it is easy to reprocess liquid fuel by any method. There is no crystal structure to get damaged. ORNL was working on physical separation of fission products like vacuum distillation when the project was cancelled. Chemical separation and isotopic separation may raise proliferation concerns and they may not be environmentally friendly.

There is a chemical separation of fuel from fission products called fluoride volatility, which is used in industrial scale for enrichment of fuel. But, it works only for fluoride salts. ORNL has demonstrated this process when they switched from U235 to U233. They irreversibly damaged the drain tanks and hastelloy plumbing by doing this. MSRE would have lasted longer if they had not done this fluorination experiment.

RE "Fluid fuel will have 50% of the periodic table in thermal gradients, plating out in heat exchangers and other cold surfaces."

Just throw away the hot leg plumbing and heat exchangers every 2.8 years initially (MSRE salt loop was circulated for 2.8 years) and increase this incrementally.
Fact: In solid fuel reactors fuel itself acts as a primary heat exchanger.
In 4.5 years LWRs throw away a heat exchanger worth of Zr tubes/cladding. Earlier LWRs threw away solid-fuel every 3 years. Why point fingers at MSR folks when solid-fuel reactors throw away stuff?
Note the difference between Inconel 625 (similar to hastelloy-N) and Zr.
https://www.tricormetals.com/cost-comparison.html