Crossover ? Passive Vs. Active

Would it not be better to crossover before amplifing the signal, or am I missing something?

better is up for debate but for an active one you need 3 amplifiers per channel for a 3 way system vs only one for passive. Good amps aren't cheap.

Speakers evolved as full range devices so you would have to change the whole culture of high end. Few speakers are designed so you can easily bypass the internal crossover.

Plus why can't they separate the highs, mids, and lows during the recording

they could but what medium would you use and where is the market? Up until the dawn of 5.1 surround and hi-rez recordings nothing could handle 6 channels. The average consumer won't accept SACD and wants mp3. Do you think they will buy such an elaborate system?

what frequencies would you choose as cutoffs? And why 3? Maybe I want a 2 way or 4 way system, and every speaker designer would want a different cutoff for their drivers of choice.

I think you are going to have to make your own recordings and build your own speakers.

Active in general is better and more control to end up with the best resolution and adjustments.. And yes of course active will rob far less power, up to 60 % less from what I understand.... No crossovers are very good to using full range drivers.

In theory, I think that active speakers make a lot more sense than passive ones if the goal is getting maximum performance out of a speaker from a technical standpoint.

However, when you go active, you lose the ability to play around with amps and tailor the sound to your liking. I guess it depends on your goals. If you like a sweeter or warmer sonud than active designs such as those from ATC, PMC, or Genelec are not going to be your cup of tea. Most active designs are intended to be used in recording and therefore are designed to be as accurate as possible.

I believe that DSP speaker and room correction is and will continue to be a great way to tweak the sound of a system to ones preference.