I think average units shouldn’t be promoted, but if they are units that need to be unlocked, maybe yes.
I think this type of mechanic would be better for ‘native’ type units, since it is a quality that encourages its use. The truth is that if this was not in the game now, if we had proposed it before, it would seem absurd and exaggerated, but I think that now many units could benefit from this.
For example the ‘Nootka War Chief’ could increase the speed and maybe the damage of the ‘Nootka Clubman’ with an aura bonus. I know it’s not the same as promoting, but it’s the kind of thing that would suit natives well.
The Tupi and Carib warriors could have poison damage, that is, damage as a result of the shot, just like ‘The Jungle Bowman’ of the Incas.
I think the promotion mechanic could be used to better balance the mercenaries, for example they could reduce their stats and population cost but allow them to get their power back with the promotion ability.
On the other hand I think that the revolutionaries of the revolutions should be able to promote themselves by default or with a card.
Limit this to units with limited number or accessibility.
Also it should only happen if the unit is initially weak (wrt cost) and lack other means of buffing. Cost effective units should not get promotions.
I think the only civ that could realistically incorporate promotions into their regular units would be the Russians. Many of their units are naturally very brittle and unlikely to survive for long and any promotions they manage to survive long enough to get would at first only put them on par with their equivalents from other civs, which is hardly a gamebreaking occurrence at all.
Other than that scenario I don’t think promotions would work well outside of their current niche of native units from Royal Houses. At least that is my opinion for now.