I guess if one is deciding to biamp, you need to insert an active crossover device.
Not really. You can use two of the same kind of amps. You don’t gain the dynamic range as well, but you get 2x the power supplies feeding the amps.
I’m not sure I understand the vs. Using an active crossover implies you will be using two (biamping) or more amps.
When you insert an active crossover device, does this improve the quality of the signal directed toward individual drivers on your speaker so as to avoid the need to biamp which is also designed to better focus the signal reaching the drivers in your speaker?
The purpose of any crossover (passive or active) is to filter the signal to each driver so that the driver works in it’s ideal range. Maybe step back first and ask why speakers have a tweeter and a woofer, instead of all from one driver.
There are multiple answers, but the simple one is that a tweeter can’t woof and a woofer can’t tweet.
There’s no single best type of crossover but the one undeniable benefit of active crossovers is power efficiency, which is a reason they are so often used in professional environments. Your total amp power can be smaller using an active crossover for the same output than using a single amplifier. Another undeniable benefit of active crossovers is you don't waste heat level matching drivers. Speaker makers are often faced with tweeters which are much louder than the woofers. With a passive crossover you use resistors to compensate for this, wasting power as heat. This isn't needed in active, you change the levels before the amplifier. No waste.
Of course, lots of other complexities, like cable and amplifier counts come into play as well, but consider that your average home theater is often at least bi-amplified, with a subwoofer and it’s amp doing < 80 Hz and the remaining speakers doing > 80 Hz.