Thanks for the interesting proposal and PR. I think it would be useful to have a way to find out if a lens is applicable to an object. not just for property lenses.
In general this is difficult to implement though, especially for user defined lenses. That is why we did not do that (yet).

Indeed this would be nice to have. Such a check is a simplified case of what we call subsumption in Turing/AbstractPPL. It gets complicated quickly... but maybe our implementation can provide some ideas and test cases for Setfield.

The functionality is useful, but shouldn't really be a method of hasproperty: you don't do getproperty and setproperty! with optics, right? :)

For Accessors optics, this check is performed by the hasoptic() function in AccessorsExtra.jl.
It can, and probably should, be upstreamed to Acceessors itself at some point – but for the sake of future stability, better to define the proper semantics first. See JuliaObjects/Accessors.jl#92 for some discussion + open questions on semantics.