This is not a very researched statement. EMG is not the only type of active pickup, they're just the most well known. As the OP said, Bartolini, Seymour Duncan, Alembic, and others make active pickups--with preamps in the housing. Note that MTD has used active Bartolini pickups for a long time in their USA basses (although I think they recently switched, but I'm not sure). Active pickups have less turns of wire and therefore have a supposedly wider frequency response.
Although EMG apparently does pot its pre-amps into the pickup which makes them active only.
I Think you are confusing active with Low impedance.
I'm sure others have potted the pre-amps into the pickup casing.
That said I don't see any compelling reasons for potting the pre amp into the pickup. I know companies can make their pickups very easy to set up, without routing the body or complex wiring, and they can conceal the circuit from someone that might reverse engineer it or tinker with it. But if any component on that potted pre-amp goes bad, you have to throw the whole baby out with the bath water.
Low impedance pickups which typically have less turns of wire and wider frequency response, normally require active electronics (vs passive) to bring the pickup signal to a usable level before sending to amplifier.
I own an Alembic Bass, with Anniversary electronics. The pickups are Low impedance, and it has a modular electronic components that have quick connect pin configuration. But the pickups are not active.
I also have an Alembic hum canceling "Strat" style, and "Gibson" style. They have no active electronics embedded in the pickup.
I doubt that Alembic ever made a pickup with the pre-amp potted into it, as they seem to be quite fond of modular and serviceable configurations.
I also have a Les Paul Triumph Bass with Low Z pickups. It originally had a matching transformer in it, instead of a pre-amp.
Can't speak for other manufacturers I'm sure someone else has potted the pre's into the pickup.
I'm pretty sure a majority or Low impedance pickups use active pre amps, but a minority of pickups are "active".