Sorry @lonemountain but high passing mains,. especially residential is often the right thing to do, and done right, with quality subs and filtering on both is inaudible. There will be no shift in tone and no localization is possible. You have to be cutting off below the Schrodinger frequency. Your subs have to be low distortion, especially anything third order and higher. That may be as much a consideration for where you're cut off frequency is as anything. If you've got large means that can play low distortion at high volumes at base frequencies, then I would consider it beneficial to run them full range. But most mains these days don't fit that criteria. For most means I would far prefer a cut off that's not full range especially if the customer likes high volume levels.
I don't understand your comment with respect to DSP. With any modern half decent quality ADC, you're not going to hear any sound of using an ADC and then DSP. And of course if it's an all digital system, it's a nonstarter. Talking about DSP delay is also not relevant when you bring up in the same paragraph 180° out of phase operation which is a delay. There are no absolutes speakers like a line array can be difficult to integrate with subs and an evaluation needs to be done based on mains speakers, room size, listening levels etc