I'm not sure how to count bard, since I like to get more (especially melee) damage by multiclassing to the point that "bard" loses its identity as such per se.
Yup. Even on their own the Sword and Valour Bards stop being casters and become melee brawlers. The line between Eldritch Knight and the "two attack" Bards is blurry ...
But that's with WotC.
Those Bards are essentially an eldritch knight more focused on (spell) damage and cc instead of mobility and defense, I can see that. My issue is more my own play style, though -- I could have played any of them as more "bardic", but they tend to lose the class feel in my hands unless I set out to do a bard in a "squishy" spellcaster role.
You can do some very interesting things with college of swords, things an eldritch knight simply can't (like decent spell saves). It still doesn't feel like a bard if you focus overly on the melee. I don't know why that is.