I don't think that a gish has ever had a chance to gain an identity in DnD, as every edition the old version is deleted and a completely new attempt brought in from scratch. Eldritch Knight, Bladesinger, Duskblade, Hexblade, Swordmage. The class concept can't even keep a name, let alone an identity.
I think it's worth querying why this has happened.
Bladesinger has actually appeared in all subsequent editions from its appearance in 2E, but it in 2E it was Elf-only, in 3.5E, it was Elf or Half-Elf only (and also kind of sucked), in 4E they dropped the race restrictions but because it was a Wizard subclass, it was kind of outcompeted by Swordmage conceptually for people who wanted to play "magic warrior" and in 5E it is once more a Wizard subclass and not great as a Gish. So being initially race-specific, then wizard-specific is what stopped this becoming the "Gish class".
Duskblade and Hexblade essentially competed against each other and both had other problems. Duskblade once more tried to make it All About Them Elves (!?!!??! WHYYYYYYYY??!?!?!?), and whilst it was a true Gish, the really dumb name + elf-centrism + not appearing until PHB2 really limited it. Hexblade, from the Complete Warrior in early 3.5E, is extremely weak, because 3.5E was godawful at balance (possibly the worst of any edition, even the ones which barely tried!), has a weird-ass theme (cursing people and swordplay is not a gish, frankly), and the similarity in name between the two caused further problems. Both deserved to be forgotten, to be clear.
Swordmage, on the other hand, was an excellently-designed, strong, original class that was a true "magic warrior" that actually fit well with a lot of fiction (both fantasy fiction and fantasy manga/anime), but would have required it's own class and some supporting spells to make it to 5E. As 5E was mortally terrified of adding any classes beyond the initial ones (which were mostly a callback to 3E), and sort to reduce 4E classes to subclasses at most, there was no chance of that happening, even though, at this point, it would be highly possible to do.
Eldritch Knight was a very half-arsed attempt to make a gish people could play without multiclassing, but in reality is just a Fighter with some limited spell support, and mostly you just want to be casting Shield a lot, and a handful of other spells that don't actually need any INT. It's only a good subclass because these spells are so inherently strong, particularly Shield, without which it would be considered pretty bad.
5E did have a much more gish-like gish in the form of the DNDNext Sorcerer, but abandoned that for unclear reasons (it didn't
seem to be unpopular, and I don't think WotC claimed it was, but who knows?).
So this isn't just some random tale of woe - there have been specific reasons this happened. Specific, frankly bad design choices that lead to this situation. Had 3E not been so absolutely terrified of allowing anyone to cast and wear armour/fight until very late in the edition, it could easily have turned out a lasting gish class, which 4E and 5E would likely have maintained, but it was not to be. Had 5E not been so terrified of offending people by including any 4E-specific classes Swordmage could also have worked out. Really the issue here is that fear or letting people play a gish, or disapproval of the concept for anyone but elves, lead D&D designers into making bad decisions.