The primary advantage of active monitors is not that they are inherently "better". The advantage is that I do not have to figure out which crossover and amp to use. I don't have to think about it, it is already done. Yes they (the designers) match the size of the amp to the driver, but I could do that myself (by buying two amplifiers of appropriate size for the drivers) if I wanted to. This is all assuming I want to bother with bi-amping my monitors (and they can be bi-amped). Active crossovers are inherently better than passive, but if you bi-amp your monitors you can use an active crossover. Active monitors are inherently better (from an electronic and theoretical point of view, though you must compare similarly priced systems) than passives which are not bi-amped.
At any rate, the main reason for the popularity of active monitors is that you don't have to think about the amp or crossover. With the number of inexperienced and untrained engineers out there these days, this is a very good thing. Even I, as an experienced and trained engineer, find actives MUCH easier.
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"Cowards can never be moral."
M.K. Gandhi