Not rare enough that you can disregard imperial age strength either.
If HC can kill their target faster and move on to the next one faster it sounds like it would reduce overkill by preventing too many HC firing at the same target.
I’m sorry for repeating myself, but if you think this bonus is UP why do you think it should be entirely canceled to make room for another one? If Burgundian had 7 bonuses like Teutons then it would be fair enough, but they only have 3. If they had 4 it would perfectly fine, there are a lot of civs that have 4 bonuses and are totally OK, so I can’t see the problem here.
This would require a separate discussion, but in my experience, seeing imperial age in 1v1 open maps (without water) is very rare. If the opponent has a better civ, (e.g. I’m generic civ, opponent is Mongols) I will ALWAYS rush them, so the games usually don’t have large enough eco for either player to even consider clicking imp.
I would personally prefer one good bonus, than a bunch of unrelated small bonuses that are hard to take advantage of. It’s very expensive to produce cavalry AND HC, so I’d rather have a solid feudal age bonus that I can gear towards a specific strength than having slightly better stats on some units that aren’t even going to see any play. I’d only ever consider making HC with Burgundians, if I am going to face Goths (and therefore Huskarls).
If I, an humble scrub, can go imperial age despite getting rushed then double castle dropped as Cuman (arguably not the fastest civ around), getting to imp isn’t that hard.
HC can be given to civs merely to combo them with their cav. For what other reason civs like Malian, Khmer or Lithuanian would have HC despite having 0 historical justification for it? Heck they even wanted HC for Bulgarian in the beta 11
And yes, I know that cav and HC cost the same ressources, but if anything as Burgundian you should have spare ressources in imp (savings on paladin upgrades+Burgundian vineyard+relic that gives gold and food) so I would rather be able to think “cool my HC have 25% more damage compared to Frank ones” rather than “uh my xbows have bracer ig?”