Mostly due to if the coils move into saturation, or basically towards their power capacity ability limits. If you're looking at a pro audio type loudspeaker cabinet design, generally you'll wind up(pun intended) using iron/steel core coils on the woofer side of the circuit, and air core coils on the mids(if any) and high frequency sections. Overkill is never a bad thing, buy the largest gauge/power rating/lowest DC resistance coils you can afford(and big ones get expensive), as headroom is always your friend in pro audio.
Yes, this. An air-core coil will never saturate. It will stay linear until it melts or starts arcing between the turns. It's also simple to design. A ferro-magnetic (typically silicon steel at audio frequencies) core coil will become non-linear at some point. It's complicated to design and you need to get suitable cores with full engineering data. By using a core, however, a lower resistance (higher Q) can be achieved for a given amount of copper. So, as John points out, they are often used at lower frequencies where higher inductance is needed and where the lower cost and weight pays off.
For hobby use cost and weight may be secondary considerations and the air-core coil's resistance can be taken into account in the circuit model. For a given style/size coil the resistance is approximately proportional to the square root of the inductance. The scale factor can be taken from a typical coils out of the Parts Express catalog, for example. Once the inductance and actual coil are chosen then its exact resistance can be put back into the model and checked.
My way around big inductors is to bi-amp, which has very many advantages. But that's another story.
My favorite cartoon about DIY was in the back of "Chemical Engineering News" many years ago. A woman in the foreground says "My husband is a real do-it-yourselfer. He's making a lawn chair from scratch". In the background is the husband with a few barrels of petroleum and some chemical gear.
--Frank
