I agree with these ideas in theory, but in practice, they haven't seemed to matter so much.
To avoid derailing this thread from the OP's question, we can agree to disagree on this.
I read that long page. The only point I'll readily agree with is that passive crossovers introduce losses in signal strength. Active crossovers avoid this. Sometimes these losses can be large, especially in the bass frequencies. As the price of amplification goes down, and the price of good speakers rise, this becomes a smaller and smaller problem.
I still maintain that a well designed crossover makes or brakes a speaker. It makes little difference whether this is done actively or passively. A poorly designed passive crossover will not sound better if implemented as an active one. And a well designed active crossover will not sound worse if implemented as a passive one. The theoretical benefits of active crossovers in home audio (I'm saying nothing about large auditorium PA systems), so far, have not been worth the additional costs of implementing it. This could easily change as costs change and new products appear in the future.
You have hit the one of the main advantages of active speakers, and that is high power.
The lower the crossover point the greater the advantage of active designs. Strictly the disadvantages of passive designs rapidly increase as the crossover point is lowered.
From a design point of view an active approach gives much more freedom. For instance a passive circuit can never apply boost, only cut. An active crossover can provide both cut and boost. So it easier to get a flat response. In addition passive designs are very limiting as to which drive units you can integrate. An active design allows you to choose any decent drivers you want.
All things being equal, if the industry could escape the shackles of the past, all speakers would be active. In car audio that has happened. All the crossovers in the stock audio system in my car are active. This is true I think, for pretty much all autos now. I believe that this is the prime reason for the quantum leap in performance of car audio systems in recent years.
In fact I would say that a huge number of home audio systems are inferior to stock car systems now, in many important parameters.
As I have said before, for the vast majority of the public, the best audio system they own is in their cars.