Had my seat tipped down on old bike. But it was an accommodation for a bike that had become too large for me (I shank, the bike didn't). It worked for me in the sense that if relieved pain to the forward sit bone. Had I not done so, the bike was unridable. So you might look at the need to lower the nose, not as something you should not do, but as a symptom of a different problem. That problem could be so slight that you just adjust after awhile and it becomes "normal." One word of caution. If you should go looking for a new bike be careful during any fitting. Your idea of "normal" may lead you to tell the fitter that the new bike feels "comfortable" (i.e. like your old bike) and you could find yourself buying another new bike replicating the same old problem.

Good luck.