Why not go crossover-less?

>Could the following be another reason the cross-over is placed in the speaker?

It's placed in the speaker because the output transformers and vacuum tubes which go into amplifiers are expensive and the speakers which play loud with single ended triode amps don't need the extra headroom in a home environment.

Without output transformers and tubes it's more a matter of tradition, marketing, and inertia.

If you're concerned about how accurate the transfer function is, the active solution is a lot better because the filters operate into purely resistive loads which don't change with output level (thermal compression) or driver position (Things like voice coil inductance actually vary).

>Would there not be an advantage to place the crossover in the linestage instead of the speaker?

Other than marketing there's no good reason not to. The cross-over function doesn't change with output level; you can use all-pass filters to match phase independently of baffle configuration; you get the same peak output level with smaller heat sinks and power transformers; big inductors get replaced with low wattage resistors (not $.10 each in small quantities with 1% tolerances), and big capacitors small ones (under $1-$2 for 2% tolerance film caps) due to the higher load impedances. Even when starting with your existing amplifier, an active cross-over+power amp+power supply can cost less than the large high-quality reactive components needed for a passive cross-ove.r

More accurate, more headroom, and lower total system cost.

My main system is actively tri-amplified, the small bedroom setup actively bi-amped until I get enough shellac on the new woofer enclosures for the tri-amp upgrade.