I think when most people say "gish", they're thinking of an arcane caster. An arcane version of the Paladin would be a very cool thing to see, since it checks most boxes, but D&D has a problem- arcane magic is better than divine magic.
This is why you can have an Eldritch Knight or Arcane Trickster that is 1/3 Wizard when Paladins and Rangers are innately 1/2 casters in 5e- divine magic is less versatile and generally lacks the same punch.
This is why most divine casters in 5e have access to divine magic, ranging from a few spells granted by a subclass all the way to the current Druid (whose spell list is really underrated, I've found, since the vast majority of Druids I've seen in play want to turn into animals and aren't too interested in spellcasting- maybe that's a regional thing, I don't know. Feels like new thread material).
It's not that there's not really good divine spells, but they're far less of them. I mean, think about it- since 2014 almost any book with player options in it has new spells for all classes.
Now go look at the Cleric. Levels 8 and 9 have gotten no, zero, nada, zilch, not a single non-core spell and there's only 5 spells of each level in existence!
But James, you might say, nobody plays at those levels, why would they need new top level spells? Go look at the Wizard spell list. Look at their 8th and 9th level spells. The list is packed and has quite a few non-core spells in it. Obviously someone feels a need for those spells to exist, and spent the effort to make them options.
I mean, if someone was making a new character who wanted to be able to fight and use magic, let's look at the options-
"Well you can be a Cleric, who can easily get the best armor and weapons in the game, and can cast 9th level spells, but they don't get extra attack."
"Or you can be a Bard who can get extra attack and 9th level spells, plus they can get spells from other spell lists- but their armor isn't as good."
"Or you can be a Wizard who can get extra attack and 9th level spells from the best spell list in the game, and while their armor is technically bad, they get Mage Armor which is like leather +2 at the cost of a first level spell slot for 8 hours, and they have this cool special feature to boost their AC by their Int bonus a couple times per day, not to mention the best defensive magic in the game."
"You can play a Paladin. Now granted, they only have 5th level spells, but they get the ability to turn those spells into bonus damage, they have arguably the best saving throws in the game."
"Or the Ranger. Also only 5th level spells, and there's not much to write home about, but you can have a pet, whirlwind attack, be invisible to most monsters- there's a lot of neat possibilities here."
"Or you can be a Rogue or a Fighter with 3rd level spells...hey wait, those are really good spells, I swear!"
Sure, I didn't mention hit points, and that certainly is a balancing factor, but I think a lot of players would be more excited about being able to do more cool things and potentially not take damage at all, as opposed to having less things to do and be better at surviving when you take hits. I don't have any data to back that up, and I'm sure I'll get lots of people saying "James, I'll have you know that I let people in my game play Fighters without a subclass and a d12 Hit Die, and everyone takes that choice, no question about it." ^-^
Lots of people play D&D, in lots of ways. I can only speak about what I've witnessed, after all.
And certainly, WotC apparently values Hit Dice highly in design, which really is the only explanation for the gulf between the Eldritch Knight and the Bladesinger.
As for the Arcane Trickster and the Bard, well, I got nothing.
But still, some of those options are not like the others, and at least on paper, sure sound better!
