If the data is actually linear or anything remotely resembling linear, then on distant points a linear model will do much better than a nearest-neighbor estimator. Whereas on nearby points, a nearest-neighbor estimator will do as well as a linear model given enough data. So on distant points nearest-neighbor only works if the curve is a particular shape (constant), while on near points it works so long as the curve has anything resembling local neighborhoods.
There are always “nearest” neighbors. You might wish for more data than you have, but you must make do with what you have.
If the data is actually linear or anything remotely resembling linear, then on distant points a linear model will do much better than a nearest-neighbor estimator. Whereas on nearby points, a nearest-neighbor estimator will do as well as a linear model given enough data. So on distant points nearest-neighbor only works if the curve is a particular shape (constant), while on near points it works so long as the curve has anything resembling local neighborhoods.