A home theater subwoofer needs to produce tremendous amounts of sub 50Hz bass with little to no driver compression. It needs to be able to withstand tons of punishment without getting sloppy, so heat disipation from the voice coil is critical. A well dampend amplifier is also a must to control driver movement.
Items like x-overs, EQ systems and phase controls are not neccessary for a dedicated home theater subwoofer (all the controls are in the proccessor).
Now for the real world. Most people are not building dedicated theaters or listening rooms. They will most likely jam the subwoofer into a corner of a greatroom and expect that there will be no compromises in bass response. For this reason I would think the fallowing is needed:
1. Placement flexibility. A subwoofer needs to be able to be corner loaded without the 40 to 60 Hz boost that typically acompanies this type of placement.
2. Some form of EQ adjustment that is automatic. Most of us do not own an RTA, so how can we be expected to know how to adjust an EQ. An auto EQ system with 6th of an octave or 12th of an octave parametic control would be a welcome addition. If it were smart enough to tell the consumer to move the woofer when it measure a signifigant destructive interfierence (cancelation) that would be great for the average consumer.
3. All the atributes that were mentioned at the begining of this post, but with more power. If you plan to use an EQ to cut output, you may need more power to reproduce high SPL.
4. Wireless 802.11 or 1394 would be nice but not imperative.