mmrassi,
737 is 3 different aircrafts. Are you perhaps flying Classic? In my 737NG supplementary procedures, no such limitation is mentioned.
Captaintcas,
I think most airlines recommend LNAV for VOR tracking (in case of VOR approach, of course cross checked with raw data in the background). For departure, cruise and arrival, we rely on Require Navigation Performance vs. Actual Navigation Performance and associated caution messages (without raw data cross check). Most of the procedures and route structure require P-RNAV anyway (Europe). I have a feeling you are flying classic too?
Personally, if I track a VOR radial not part of a VOR approach, it will be with autopilot and FD off, for fun/practice (and not with AFDS VOC/LOC).