Wriggles also gave armour and a free ward every 3 minutes. It was the armour in combination with the lifesteal that made Wriggles such a strong lane item (and the ward didn't hurt either). I agree, we may see Cutlass being built as a first item now, but I feel like it's going to be more for the active enabling a kill rather than for the sustain.
It doesn't matter what the current meta is. Bruisers are always going to want to build tanky at some point unless they're ahead because otherwise they will explode in teamfights; the previous version of BotRK was actually FAR better as a bruiser damage item than the current version, since it gave you damage that scaled off of your opponent rather than your own stats, allowing you to build uber-tanky and still gain its benefit. I actually think that BotRK is slightly OP atm, but it's certainly not because I think it will make bruisers stronger at the expense of other roles.
That's the key here: "At the expense of other roles." If you give a bruiser and a ranged carry a BotRK, the ranged carry will gain more benefit from it because the bruiser has more health to shred, and the carry has more AD for the lifesteal. This means that just because the bruiser can use the item, he isn't pushing AD carries out of the game by using it. It also directly counters him, and doesn't counter the ADC, so when both roles use the item equally the ADC will still come out ahead.
I'm not saying "If you build this item on a bruiser you're an idiot and should go die in a fire." What I'm saying is, it's not really a big deal if bruisers build the item, as it's still solving the problem it was designed for.
EDIT: Also, in regards to Jax, of course he loves the item, he actually wants to build a ton of damage and get free defensive stats from it. He's much more of a carry than a bruiser, always has been. He supports my point that people who already build AD like the changes, and people who don't build much of it don't really care.
Most bruisers don't build a ton of AD, Jax is an exception.
As for the two iterations of BoRK. The damage portion does not change a bit beyond trading 15 ad for 40 AS.
Part of why the whole "warmogs stack" meta is toxic is that it gets people too tanky to be burst by burst ap/ad champs. If your "cure" to warmogs stacking is an extremely statistically efficient item that ADCs and bruisers can use - those burst casters aren't going to be able to use it. If the sustain is high enough - the bruisers just sustain through the burst and it equates to the same thing.
Irelia had her sustain nerfed from having 26 onhit damage - At the level you can get it by - BoRK gives 1.5x as much sustain as irelia's passive per hit.
If it gives that high sustain - and transitions cheaply from an item you already said will become a good laning item - its going to be rushable by bruisers.
For 1300 gold from cutlass - BoRK gives 5% current hp on hit(roughly as good as 2.5% max hp damage), 40 AS, like 2-3x as much sustain as cutlass, and a huge hp-nuke + increased duration buff to the active.
I'm not saying bruiser BoRK >>>>> adc BoRK and it will do the job of shutting down hp stacking - but a moderately cheap item that gives insanely good sustain and good DPS will create the same kind of power bubble that hp stacking currently is.