As a confirmed and persistent military historian (what, you hadn't noticed?) my problem with all the Unique Units as they are presented in the game now is that they are associated with a Leader or Civ regardless of the In-Game situation.
So, an England in the middle of a Pangaea continent gets a Sea Dog
A Mongolia on a small island with no horses gets Keshiks
How useful . . .
This problem also persists with all the Uniques that are permanently tied to a Leader or Civ, but (to me, at least) it is most pronounced with Unique Units, many of which are, or their unique attributes are, tied to the terrain they are trying to maneuver and fight on, and it has persisted as a Game Mechanic in all the Civ games: if your Civ is tied to a given terrain/climate for its advantages, you are SOL if your start is in any other terrain/climate. I have quit counting the number of times I have stopped trying to play the game I wanted to play after restarting with England or Norway 6 or more times and never getting a start anywhere near any coast.
So, I think every Civ needs some kind of choice or alternative Unique Unit(s) to allow for Utterly Non-Historical Starts. And I think the option to change Uniques in some way should be present in the game.
Because the game will inevitably include Civs without a wide range of Unique Units applicable to multiple Eras or periods of the game - let's face it, if the game includes more than 20 different Civs, one of them is going to be America/USA with access to only the late Eras of the game historically, or Rome that has access, historically, to only one Era (Classical), then some 'creative' Uniques will have to be included.
Generic Uniques sounds like a contradiction in terms, but it isn't: "Generic" in this case means available under certain conditions to any Civ, "Unique" means the Unit has different attributes or additional attributes compared to the Standard Units in the game.
An Example:
Spearman is a Standard Unit in the game, available to anyone who knows how to work Bronze (yes, there were much earlier warriors/soldiers armed with Spears, but the first indication of Spearmen in a dense, organized formation of ranks and files that can fight off any mounted troops dates from the beginning of the Bronze Age in Mesopotamia).
Hoplite - the 'standard' (or at least Perennial) Greek Unique Unit, Classical Era or its equivalent in Civ VII
Immortal - the Achaemenid Persian Unique (Infantry) Unit, also Classical Era
Fyrd - a potential Anglo-Saxon Unique Spearman
But "Spearman" in variations, are found everywhere that Cheap Infantry are required, which is nearly everywhere. So, there are numerous variations on the theme of "spear" from which Generic Unique Spearman Units could be designated:
Peltast - Spearman with a bonus movement in rough terrain
Dagger-Axeman (Ji) - a primitive Halberd: Spearman with less malus against Melee Units.
Lugged Spear - a Spear designed for fencing and parrying, so also less Malus against Melee Units
Half-Pike - an extra-long spear held in both hands, but about 2/3 the length of true Pike: men with different weapons, like swords or bows, can stand in front of the 'spearmen' and still be protected by the protruding points, so this unit provides an Anti-Mounted Bonus to adjacent units.
Each such Generic would have very specific conditions for its selection, but they could be selected by more than one Civ if the conditions are met: the Half-Pike was used, for example, by Sumerians, Chou and Han Dynasty Chinese, Picts, Scots and possibly Greeks, the Lugged Spear by Germans, Romans, and Chinese, the 'Peltast' type by Greeks, Thracians, Romans, Persians, and almost all of the various 'semi-Barbarian' (they could be depicted as a Civ or Barbs) Gaulic groups in modern Spain and France and the Germanic tribes in the early Classical Era.
So, the fact that you are playing America and your Unique is a P-51D fighter aircraft that you won't see until the Atomic Era doesn't mean you are Unique-less until then - American Lugged Spearmen can be marching around in the Classical Era under their Mullet and Stripes banners . . .