It seems to me the warrior and the weaponmaster can exist side by side with each other as long as both can contribute. One's just a streamlined version of the other. That sounds like exactly that 5e is trying to do.
Swordsage no. Swordmage sure, why not?
The difference mechanically isn't much, but thematically it's important to me. I'm okay, in fact, enthusiastic about character classes like the swordmage who combine martial training with magical expertise to create a fighting style that might include flight, or teleportation, or making your sword burst into flames.
What I don't like the idea of, is a class that gains those abilities explicitly through training long and hard with the sword. If it's possible in the world, to train with the blade so long and hard that you can make it burst into flames or balance on bamboo branches, what does it say about the swordsman who can't do those things? It says he didn't train long and hard enough.
A magical swordsman who is explicitly a blend of martial and arcane training I'm a big fan of (though what I prefer to the swordmage is the old-style fighter/magic-user).
If your intention is to have a Kung Fu/Wuxia style campaign where enough martial training really does let you fly, deflect a hundred arrows at a time, or any of the other things that you see in Asian fantasy movies (and a lot of Hong Kong inspired western fantasies as well), that's cool too, but then you don't need the swordsage then either. You need to give those powers to the warrior and weaponmaster.