Reprocessing increases net efficiency considerably [1]. Few people do it since uranium is very cheap relative to the amount of energy extracted from it, even without reprocessing. But if fuel ever becomes constrained, reprocessing would become competitive.
Nuclear weapons proliferation isn't a risk among most countries that have nuclear generation programs. Heck, most of them already have nuclear weapons. The rest can contract out reprocessing to nuclear-armed countries.
Also there are "near-breeder" CANDU heavy water moderated reactors: they are a proven technology that exists today and can use non-enriched uranium. They also in theory can use a plutonium/thorium mixture, so can burn thorium.
They are cheaper as far as fuel, but it turns out that fuel didn't become as expensive as anticipated in the 1970s (when it was thought that there would be 1000s of reactors). They are physically larger, so have a higher construction cost that put them at a disadvantage compared to conventional LWRs.
The tritium needed for fusion reactors comes from these CANDU reactors (some of the deuterium from the heavy water is converted to tritium, it is collected).
Nuclear weapons proliferation isn't a risk among most countries that have nuclear generation programs. Heck, most of them already have nuclear weapons. The rest can contract out reprocessing to nuclear-armed countries.
1. https://en.wikipedia.org/wiki/Nuclear_reprocessing