DEQX does both speaker and room correction, separately. I greatly prefer the DEQX system which is more like the TacT system I am use to. I do not yet know how much manual tweaking I will have to do. As far as room correction is concerned, there remain issues that have to be handled acoustically. The room has to be in tolerance or you will just clip filters. The types of loudspeaker being used are also important. Certain speaker designs have far less room interaction. When it comes down to brass tacks there are two major types of errors, errors in amplitude and errors in time. These are easy to correct for, to a point. You cannot correct for echoes. There are problems that have no analog solution. Other then by shifting position there is no analog way to put a delay on a speaker, and the dimensions of the room and other practicalities put severe limitations on how far you can move anything.
Yes, you can do an analog active loudspeaker. The only good reason to do that is you do not have the engineering to do it digitally. Digital signal processing including crossovers is, in every way, superior to analog signal processing. Analog signal processing is about as useful as tits on a bull. The only exception is in the mind of the audiophile. Audiophiles are as change resistant as cyclists. It took a decade for the cycling community to accept synchro shifting.
As for the type of amplifier that again depends on the loudspeaker, even the independent drivers can dictate amplifier choice.