I agree with everything PolyGeo said. It also depends on what precision you are aiming. For example in chile (37° south), in worst case I have 3cm distortion every 100m. Too much for surveying. You can also transform: UTM >> geographic >> ECEF >> NED

I agree with everything @FSimardGIS commented:

The UTM grid north does not match True North except on the central meridian and Equator. There can be a difference of a few degrees. (This is called Grid Convergence) Moreover, UTM being a Projected Coordinate System, you will have distance distortions if you use those coordinates (although quite small within 3° of central meridian). And the Z (Down) coordinate will be wrong with UTM because it wouldn't take into account the curvature of the Earth.

It also depends on what precision you are aiming. For example in chile (37° south), in worst case I have 3cm distortion every 100m. Too much for surveying. You can also transform: UTM >> geographic >> ECEF >> NED