Is 'Non-Catholic Non-Orthodox Modern Western Denomination' an ok definition of Protestant?

One meaning of the term "Protestant" is "a church drawing its roots from the Reformation and the denominations of the Reformers in particular". I have also seen the term extensively used to mean "a modern non-Catholic non-Orthodox western denomination" with 'modern' meaning dating back no earlier than roughly the time of the Reformation and 'western' generally meaning embracing western scholasticism and enlightenment thinking in general. I have recently been told that the latter meaning is "just wrong". Is the latter definition 'wrong' in some fundamental way and what reasons are there to use or avoid using it? If it is wrong, what term (not "modern non-Catholic non-Orthodox western denomination" please, that's just way too long) would be better for this broader usage?