>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.