Whilst the VOR adequately meets the accuracy to support RNAV 5, it does not provide the level of accuracy to support more demanding navigation specifications.
If we consider a Doppler VOR with an NSE of +/- 2½ ° and apply that performance using the 1 in 60 Rule, we note that the maximum range at which the VOR can meet a 1 NM performance is 23 NM. Please note, that certification to any navigation specification is based on the Total System Error of which NSE is one part; Flight Technical Error (FTE) and Path Definition Error (PDE) are the other two.
Therefore, a Doppler VOR will not support a 1 NM lateral performance outside of approximately 15 NM.
This is why the only Navigation Specification that uses VOR is RNAV 5.