This is an important consideration in practice, and I think it would be helpful if classes teaching O-notation would include an exercise that makes this point. It is also true, however, that O-notation considerations always dominate for large enough problems.

Anyone expecting the O-Notation to give the outcome of measured performance has made a category error, as it is never about run-time itself, it is about the change of run-time with problem size (and only in the asymptopic limit).