I too agree that Brits have quite a poor chance against Goths.They only have normal champions and weak cavalry.But Huns don't deserve their tarkans to have any bonus vs infantry.Look at these contrasts:
Cataphract:good vs all infantry and cavalry counters,weak to pierce attacks and building fire
Tarkan:bad vs meele units but excels against buildings and good vs archers.
There is the clearly defined role of Tarkans:against pierce units and buildings.Afterall,they have awesome CAs to counter the infantry and halbberdiers that threaten their four-legged armies.If tarkans get bonus vs infantry it would be massively overpowered.
As for Huns vs Goths,they can easily form an infinite meatshield of hussars with CAs backing them up.Do remember that Huns are mostly picked on open maps alone where they have a good chance of taking out/weakening the eco of the Gothic player before imp where the industrial production of infantry starts.
1 Tarkan by no changes by coast/HP/melee with Infantry Bonus get OP against F.E. Goths, that i agree. So would Goths get the same unbalanced like Vikings vs. Huns. and other infantry civs would get a hard knock life, not good idea from me
So would get better a mostly underused Slinger for only few cases as fair Option OR give some Civs a Hidden Melee vs. specific Units like Cataphracts vs. Camels, Genuese GBM
F.E. Slavs Bojars and Infantry get a bad Fight in Castle against Chieftains Berserks and Archers, same vs. Incas, Japanese, Teutons (DM).
Britons (this Civ is besides vs. Goths a special Case :D ) by no affected 20% faster (like aztecs no 15% affected by trebuchets) Slings would get fair diffences by Units like Mayans vs. Goths, here is by LBM with Bonus vs. Infantry same problem and get Japanese unbalanced vs. Britons.