I suppose this depends on your definition of "nontrivial", but I don't think most would, unless you count the fact that some stuff in std is implemented with unsafe under the hood. The only times I've ever needed to use unsafe Rust code in 5~ years of writing it professionally was for interfacing with a vendor-specific C library, and that was only for the wrapper around it; the rest of the code didn't need to use unsafe.
Yes I'm probably biased towards seeing more unsafe as a deal with a lot of wrapper libs (crates which in turn have -sys crates and so on). Looking at the dependency graph, if I use 10 deps directly and 5 have unsafe then that might be 50% of the direct dependencies, but probably just a small fraction of the total including transitive.
