In theory, direct connection from a power amp to a driver is superior. Damping factor is optimal, resulting in greater dynamics and faster transients. As you mention, power requirement drops significantly. A passive crossover has to drop the level of each driver to match the least sensitive driver. For example, say your tweeter is 92dB/W/m, mid is 89dB, bass driver 86dB. You would lose 6dB to resistors, and instead of a 25W amp, you need 100W just to equalize driver sensitivity. Then you'll need baffle step correction, generally 4-6dB. Now you need ~300W for the same level as your crossover-less 25W system.
In the real world however, an active system is no panacea. I have tried to go active with a Marchand XM44 electronic crossover, Marchand XM46 passive line-level crossover and FMod modules. None were transparent, all compromised the sound of my amps. I then tried a single high quality cap on the input of my power amp to roll off the bottom end by 6dB/octave at 80Hz, relieving the monitors of the bass range to cross to a sub. The cap did what it was supposed to, it relieved the mid-woofers of deep bass, but caused grit at high frequencies, a bad trade. You are going to hear anything inserted between a preamp and power amp. The crossover had better be at least as good as your pre and power amplifiers.
You need to know something about speaker design to implement an active crossover. Simply ripping out a crossover and substituting an active crossover is almost guaranteed to fail. Mid and bass drivers often need a notch filter to deal with resonance above their operating range. Even with an active system, speakers need baffle step correction. Then there's time alignment, a tricky problem, compounded by the acoustic slope (natural roll-off) of the drivers and the electronic slope of the crossover. Speaker design is complicated, whether active or passive.
Amps are not cheap, nor are cables, and IME they need to extremely well matched for anything above the subwoofer range. Some people seem happy with different amps on their mid, tweeter and bass drivers. That was just awful to me. It was easy to get better bass and treble with non-identical amps, but coherence suffered; it was hi-fi sounding, not musical. I gave up on active crossovers. I run my main speakers full range, with subs connected in parallel and DSP corrections on the subs only.
A DSP solution with convolution filters, auto-eq software like REW or Accuphase and a USB microphone may be an ideal solution for someone with a fully digital system. I looked into it but haven't gone much further. It's a steep learning curve, and my system sounds so good to me right now that incentive is low for another audio system battle.