They were nerfed in different areas.
You want to increase their speed so that they can kill melee cav when the area that they got changed on was something completely unrelated. Their ability to kill melee cav has not changed, at all since TAD.
You called them strong in TAD when in all the areas of comparison you want to make, their ability to catch melee cav, being kited by dragoons, their stats comparison vs dragoons, their lack of multiplier vs artillery, none of these things has changed at all since TAD. Both dragoons and ERK got their ranged armour reduced.
The recent DE changes even made it so that it took less damage vs skirms they they used to (they used to take pure x2 from skirms in TAD).
If your argument is that they are now bad with 6 speed compared with their stats in TAD, atleast based it off something that actually changed. You dont make changes to a unit by going “well they were too strong in this area so we are nerfing it, but lets just buff this other area that werent a problem before” that would be like since cuirs splash is strong, lets reduce that while giving them siege damage cause it was kinda.
If you think they are bad, then the obvious answer is maybe reduce the negative multi to 0.8 instead of 0.75, maybe change it to light infantry instead so they kill muskets better. a 1.5 multi against artillery if you think its so bad at doing that.
then why make the video of the kiting comparison then?
Why have your starting statement about comparing their stats? and how they get oneshot by goons in an equal numbers engagement?
How does “they die to goons” go to “buff them against melee cav”?
The change you are proposing would change nothing about why you think they are bad, they still get kited by goons, they would still not be better at attacking artillery, still not be as good against range infantry. And unless they are also 7.25 speed, they would also not be as good as goon in chasing cav.
and yes just about most of the range cav would let melee cav escape (only yabusame and cav archers currently have higher speed then most melee cav) cause their animations allow them to escape the target lock if its long enough.
They are fast DPS unit that acts as defensive screen against charging enemies, say by kiting enemies, defending ally cannons, backline dps when enemy is snared, you know the normal roles of a light range cav.