Since launch the KvK arenas have been dead.
Unlike in the TV shows where Klingons seemingly like to fight each other all them time, most STO Klingons seem to prefer the explosions from Fed ships over their warrior brothers...
Even during the Glory days of PvP arenas in the first 6 months of the game, there was never more than a couple at best in the KvK qeues...the FvK qeues were packed.
AMS is only an inconvience now becuase it has a proper counter to it. If one does not have that counter then it is still very discouraging to be hit by it.
energy syphons = energy siphon the skill
tachyon drones = tachyon beam = Beam target shields
theta-radiation = Eject warp plasma without the damage + perception debuff + small crew damage
aceton assimilators = aceton beam/field + crew damage(??) + energy siphon
bio-neural trics = Tricobalt torpedo + Point defense system
graviton pulse = Tractor beam + small chance Beam target Engines
Some of these may need a looksie since being skilled in thier use and having the right equipment can boost them to very high stats, but almost all of them can be replicated by use of multiple pre-existing abilities and countered by the pre-existing abilities.
Most klinks prefer to fight ourselves and rival houses in N'vok then do the KvK ques, which take too long to pop.
Back in early Season 4 before most of LF/SoS left we would queue for FvK CnH, FvK Arena and K v K Arena and the hundreds of matches played the KvK popped maybe 2 dozen times. I am sure it would have been more but I did not want to wait a couple of hours so 24 out of 500 matches = 5% pop rate.