The “baffle” is the front of the cabinet. The part that the drivers sit in.
“Disappearing” is generally defined as sounds coming from an imaginary soundstage rather than the speaker. If you close your eyes and point to the sounds and what you’re pointing to is the speaker, it hasn’t disappeared. If it’s done really well, you don’t even need to close your eyes. The soundstage goes beyond the boundaries of the speakers and it’s as if the music didn’t originate from them.
The larger the baffle, the more diffraction. The more diffraction, the more loss of fidelity and, the easier it is to localize the speaker. Diffraction is when the sound wave wraps from the driver cone back and bounces off the baffle and comes forward towards you (sort of like an echo of the original wave). It looks like this (this image splits what I call diffraction into two - reflection and diffraction):
The main advantage of a 3 (or more) way speaker is that all the drivers play a narrower frequency band. This takes a lot of stress off them and reduces distortion. You get a dedicated driver for bass, midrange and, tweeter.
Speakers are not like cans where a single driver can handle the entire spectrum. Mainly because to reproduce bass frequencies in a room vs the tiny space between the headphone and your ear, you need to move a lot of air. If you put your headphones in the middle of the room, you’ll hear all the highs, most of the mids and, none of the bass - the driver simply can’t move enough air.
So, to move a lot of air, you need a big driver. Big drivers are heavy and therefore can’t move fast enough to play high frequencies. So you need more drivers.
Compromises are all encompassing. Each company and/or their speaker designer(s) have their own idea of what attributes are most important to them and what compromises they’re willing to make.
As mentioned above, find a speaker that matches your preferences (just like with a headphone) and don’t worry about the rest. It’s like being in love with a dynamic headphone but worrying that it’s not a planar - there’s no point.