Yep this right here. 'Does magic and weapons' isn't a class, no matter how much people want it to be. The challenge is trying to integrate everyone's view of a gish into a single class, as over the years people have formed their own preferences.
- Bladesinger and duskblade had a very elven themed approach, with a strong focus on 'general' arcane magic.
- The 4e swordmage pushed genasi as their archtype, which has the potential for a strong elemental theme (which is something very ignored in 5e).
- And then tons of people talk about 'death knights' when the topic of swordmages comes up, though I'm unclear if this has the DnD or WoW death knights as the focus. Due to paladin's strong theme and basically no subclass theme/mechanics, the oathbreaker utterly fails to feel like a death knight class.
- And finally is the girthyanki gish, a psionics based teleporting swordmage.
How do you fit all that into one class?
I do wonder if going down the artificer route (the opposite of the paladin route), with extremely strong subclasses both in theme and mechanics is the best option for this.