Some may remember A.L.S.O from the early to mid 80's. Active Loudspeaker Standards Organisation. Some did try to make them more popular and IIRC ARC, Linn, BLQ, A&R and a few others were members. Some made "plug in brick" passive crossovers that could be simply unplugged when the owner was ready to upgrade to active.
It will generally be more expensive to make a decent active system simply because there is more than one power amplifier required, plus an active crossover. One cannot/should not try to save money in other areas because quality drive units and well braced, properly designed cabinets etc are just as important in an active speaker as in a passive one.
Power amps may/can be a bit cheaper than expected as
the losses from passive crossovers are gone and so amps for an active system rated at 100W in total (one amp per drive unit remember)
will often give the same max SPL as a 200W+ amp used passively. Also in an active system the amps can be tailored to their application and so
one may use 100W for the bass driver, 50W for the mid range driver and only 15W for the tweeter.
If the 100W bass amp clips it doesn't effect the other two amps and so A/ will be much less noticeable and B/ won't damage the mid or tweeter drivers.
Provided you know what you are dong in terms of matching gains, input impedances and phases of amps (or can engage someone like myself or a helpful DIYer to assist) then yes y
ou can use say a big SS amp on the bass with a class A SS amp on the mid and a SET on the tweeter... a tweakers paradise in that way!
As the bass amp would only be working up to say 600Hz in such a set up, it should not matter if you choose an amp known for incredible slam and bass control but normally let down by a rough top end... it's not driving the mid or tweeter.
Just a few of the many "hidden" advantages of active above there
Some more? OK then...
Each amp being directly connected to an individual driver sans passive crossover means it can control and grip that driver much better than in a passive set up.
Not only that but it can control it outside its passband i.e. if a bass amp is electronically crossed over at 600Hz to the mid driver then although the output of the bass amp is rolled off above 600Hz it is still giving its full damping factor and "grip" at say 1100Hz, where there may be a resonance of the bass driver. The same applies to the other drivers of course.
Steeper slope crossovers can much more easily be designed and built using active techniques and with much tighter tolerances. The higher the order of a filter the more sensitive to component tolerances it gets and with the 10-20% type tolerances common in parts for passive crossovers it can be difficult and expensive to even approach the accuracy easily achievable with active crossovers.
Time alignment is much easier and this plus similar techniques can be used to help control the dispersion pattern of the speaker, or even make it adjustable I guess...
It's a wonder passive crossovers are even used in hi fi of any real quality pretensions... is the (correct) conclusion you will see in many or most treatise on the subject...