The British and French have far more experience of reprocessing than the US and neither has managed to turn their businesses into profitable entities. The last time anyone in Britain looked at reprocessing it was with the view of determining if it was worth continuing at all. I suspect if Sellafield wasn't such a major employer in an area with sod/all other employment it would have been closed down by now.
As for why America never went down the reprocessing route, it was in part because they had a separate plutonium production industry based at Hanford. Their power industry quickly standardised on BWR and PWR systems using enriched uranium and long burn times producing relatively little bomb-friendly Pu239.
The UK on the other hand went with Magnox and AGR stations consuming natural uranium with on-load refuelling after short burn times. Their reactors produced plenty of Pu239 and the Magnox fuel HAD to be reprocessed because it corrodes rapidly.
So yes, reprocessing kind of makes sense in getting the most out of the fuel, but it won't make for cheaper energy and it will make for a lot of high-level actinide waste which will have to be processed and stored. Good luck with finding a permanent solution for that.