Comparison With Coordinate Basis
Coordinate basis vectors have the special property that their Lie brackets pairwise vanish. Except in locally flat regions, at least some Lie brackets of vector fields from a frame will not vanish. The resulting baggage needed to compute with them is acceptable, as components of tensorial objects with respect to a frame (but not with respect to a coordinate basis) have a direct interpretation in terms of measurements made by the family of ideal observers corresponding the frame.
Coordinate basis vectors can very well be null, which, by definition, cannot happen for frame vectors.
Read more about this topic: Frame Fields In General Relativity
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