My ideal list for a 5.5e class list (different from what I'd have for my ideal 6e class list):
Artificer
Barbarian
Bard
Cleric
Druid
Fighter
Monk
Paladin
Ranger
Rogue
Sorcerer
Swordmage
Warlock
Warlord
Wizard
Swordmage and Warlord are the two I've added.
Though 5e has piles of gishes, every single one has managed to not be an arcane spellstriking gish like the ones in prior editions. Instead either lacking the mechanics (eldritch knight, bladsinger), or having tons of pre-existing thematic baggage like patrons, robot dogs, swearing oaths, being musical, etc. Which also comes with a spell list which doesn't suit an arcane/elemental character. (bladehexlock, artificer, paladin, ranger, bards). 5e has yet to have a gish which behaves anything like their 3e, 4e, or pathfinder counterparts.
Warlord as martials are quite frankly an afterthought in 5e. 11 spellcasting classes vs 4 pure martials. And none of those martials is a support type martial. Warlord provides the martial equivalent of a caster, without having to have awkward reflavouring. "my spells as just me shouting orders".... which are somehow counterpspelled and don't work in an antimagic field. Battlemaster fighter provides some of the warlord traits, but in an extremely watered down way. A warlord never had to swing its weapon at all with many builds.