D&D had multi-classing a long long time where spells for a swordsman had next to nothing to do with him being a swordsman ie that has existed a long timeSee that's the beauty of it. For me it was the exact opposite. I always envisioned a swordmage as someone who " happens to hold a sword in one hand while using the other for weaving of spells."
The swordmages magic being distinct out of the box and not exactly the same stuff every caster does is why I feel more supported than yourself in that regards. D&D has always allowed flexibility in flavor and it works up to a point I felt the Swordmage brought something new to the table out of the box a sense of deeper integration (for one thing Intelligent Blademastery the attacks based on Intellect).
And the Eldritch Knight really doesn't do much any of it for me the magic seems obviously pasted on.
Additionally that flavor one hand magic one hand weapon (if not necessarily effectiveness) is served so easily in 5e ville just by taking levels in 2 classes, shrug. The 5e flavor one is still primarily using brawn and muscle power to make his weapon use work.
Hybrid does I think make a much better match though plying the MC especially if you were picking up rituals ought I think gets a long ways there. (while completely functional)That's exactly how I have flavored my 4e swordmage.
Hybrids finished popping the top off in 4e character design flexibility.
Hybriding those two really works ummm almost too well, and really does give more of that duality to you.
Fast thinking renaissance man who analyses everything tallying up scores almost in advance but also after the fact and who's approach even in physical arenas is highly unusual ... but sure dashing when the situation arises . /bowsAlso why I took the wizard MC feat (would have done a Swordmage/Wizard hybrid if the rules for hybrid classes had been out at the beginning) and heavily flavored and roleplayed him as much as a boring academic who answered the most simple questions about magic with a lengthy boring rant about the basic "maths" behind the most exciting phenomenon (I sure had maxed my arcana skill to 11, would have gone for Sage of Ages if I had ever reached epic levels) than a dashing swordman
Alek CorDaren will also be found jotting notes in the margins of his inherited book of techniques.