It is my belief that Berserker's nerf was... a bit too much on the extreme end. While it'll still be useful in some content, in my experience against higher level content, it was primarily defined by its ability to ramp up attack speed against enemies you couldn't kill in 1-10 hits. The Wolf of Saturn Six is a good example of this.
You've taken a mod that could scale up at any time, and have made it that to actually achieve its function, you have to do something that you may not be capable of getting with its limitations. Granted, enemy levels would need to be pretty high, or the enemies in question would need to be pretty tanky, but it has effectively been locked out of extremely high-end content, a good number of bosses and mini-bosses, as well as more than a few mega-mooks and special enemies.
The whole point of attack speed is to actually attack quickly enough to kill enemies in a reasonable timeframe. If you have to kill the enemies to get that attack speed, then the mod's value is moot. The same criticism could be made of mods like Bladed Rounds, which also require aiming at the same time, reducing your field of vision and mobility.
The obvious solution is to use it alongside a non-conditional speed mod. Primed Fury is out of the running, so you might as well use Quickening, or Gladiator Vice.
But then the question becomes... if there's a cap on how quick you can attack, and there's a cap on how high enemy levels can get before you simply cannot maintain your speed boost within the timeframe allotted (since you could easily lose it just by having to travel through the map, which happens regularly), why would you not simply pair those aforementioned mods with Primed Fury and have frontloaded attack speed at all times?
My suggestion for Berserker is: +20% Attack Speed; Combo 8x or Above: +20% attack speed; On Kill: +25% attack speed for 12s.
As well as a Primed Berserker Fury where the first two modifiers are the same, but the On Kill bonus is +35% for 16s.
This would allow there to be a baseline boost from the mod (as expected from a Fury mod) as well as a conditional boost that is not tied to actual kill speed/maintenance, and a way to unlock its full power. It would suddenly be more comparable to Quickening and Gladiator Vice in terms of access and utility, instead of being relegated to being more akin to Spring-Loaded Blade, where it exists, but there's simply better options.
In the end, though... if we're locking one attack speed mod out of being used alongside another, does that not set a precedent? If we look at Fury, Gladiator Vice, Quickening, and Berserker all as contemporary mods, then, aside from the base Fury, all of them offer similar-but-different bonuses for 9 Mod Power. Berserker gave the biggest attack speed, but had ramp-up and ramp-down via conditional activation and a timer, Quickening gave the strongest non-conditional attack boost alongside an extra boost that aided attack scaling, and Gladiator Vice gave extra attack power via criticals. All of a sudden, one of them isn't playing nice with the other, where they all used to live in harmony.
Primed Fury existed, and in function it largely had the highest non-conditional attack speed boost, but also cost the most. I've suggested Primed Berserker Fury to exist. I will now make more suggestions.
Quickening Fury: Quickening, but can't pair with other attack speed mods. Gladiator Fury: Gladiator Vice, but can't pair with other attack speed mods. Primed Quickening Fury: +45% Attack Speed, 35% Combo Count Chance Primed Berserker Fury: +30% attack speed, Counts as two Gladiator mods (+20% crit chance scaling with combo)
This essentially guts Melee's ability to ramp attack speed up to max via mods alone, thus lowering its upper attack speed on average without assistance from warframe abilities, arcanes, or other such outside forces. This provides an effective nerf, but on the other hand, having three new buffed up mods to compete for the Attack Speed space alongside Primed Fury, all each with their own relatively appealing bonuses, would help to spruce up modding variety, no?