I've played well over 3000 hours of this game.
I would enjoy playing an Eldritch Knight that used Int instead of Str or Dex.
I think that would make for an interesting character. And I don't think your suggestions of what "I probably actually want..." are accurate.
Nor do I think your example about a wizard doing melee damage is the same thing at all.
The Eldritch Knight is a warrior who can cast some spells. Note: there's no weird warlock "catch" to it. It's just a warrior who can cast spells. Which spells *you* think the warrior should cast may fit your playstyle. It's not necessarily mine, though, so I'm not terribly interested in hearing how the class *should* be played. I know perfectly well that I'd enjoy a high Int Eldritch Knight character, one with a high spell attack and save, along with an impressive melee attack. I've given up battle master maneuvers, after all. Now I have some spells instead, and I'd like to be able to use them. All of them and not be forced to pick just the ones without saves or attack rolls.
As for whether or not a Fighter/Wizard multi would be better, shrug. Maybe someone wants that third attack and fourth feat.
--the point is, it's a valid suggestion. it's a good suggestion. i support the suggestion. This is the kind of feedback that gets Eldritch Knight closer to where people want it for the sake of the fantasy. I don't understand how trying to tell the OP to play another class instead--which isn't the same thing--is reasonable. Or more importantly, helpful.