The physics favor separate bass enclosures.
The best locations for higher frequencies (as close as possible to the listener to maintain a higher ratio of direct sound to the reflections without being too close for the drivers to integrate correctly) aren't the best locations for bass (where you get minimal interaction with room modes and are close to boundaries so that you aren't getting nulls where the bass driver is odd multiples of 1/4 wave length from the boundary).
More bass sources also produce more uniform bass response, especially over multiple seats. Floyd Toole does a great job summarizing this in _Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms_. Earl Geddes and Duke LeJeune of Audio Kinesis sell commercial systems that work that way.
Due to cosine alpha polar response (-3dB @ 45 degrees, -6dB at 60, -12dB at 75, and theoretically no output 90 degrees off axis although a -20dB null may be more typical in practice) dipole bass doesn't couple to a room's height modes, has weaker coupling to the width modes depending on toe-in, and some effects on length effects due to the rear wave being 180 degrees out of phase with the front where a conventional speaker's bass response has essentially the same amplitude and phase at all angles. Unfortunately, this comes at the expense of dumping a lot of displacement into the acoustic short circuit - a 14" deep speaker takes 2X the displacement of a monopole to produce the same SPL at 80Hz, 4X at 40Hz, and 8X at 20Hz. That big stack of drivers gets expensive, and the alternative of doubling enclosure size instead isn't practical.
Subwoofer problems come entirely from the implementation.
Achieving a correct acoustic cross-over is often an issue.
Amplitude changes imply phase changes, including those coming from the mechanical high-pass at the bottom end of a driver's output and the analog filters in cross-overs.
The net result is that when you mix an arbitrary sub-woofer, main-speakers, and cross-over frequency the combination does not sum flat.
Siegfried Linkwitz has a nice on-line example:
http://www.linkwitzlab.com/frontiers_5.htm#T
Until recently (DSP manipulation of phase and amplitude has gone mainstream with Audyssey) most consumer gear has not included the tools necessary to address that, and this is still lacking in the minimalist gear sold to the audiophile market.
THX works around the problem in the home theater environment by specifying electrical and acoustical filter functions that sum correctly - 4th order Linkwitz Riley low-pass on the sub-woofer, 2nd order electrical and acoustic high-pass functions for main speakers.
REL works around it by providing an adjustable low-pass that can be adjusted to mate well to the speaker's mechanical high-pass function, although this does not relieve the speakers (especially 2-way ported designs) of low-frequency content that can cause distortion problems.
Some sub-woofers have problems.
Non-flat tunings are often used giving them a one-note character.
High distortion, port noises, and shallow slopes can lead to sub-woofer localization.
Many sub-woofers aren't good matches for smaller rooms.
Pressure sources have increased output as frequencies drop bellow the room's fundamental resonance (the speed of sound which is 1130 feet/second or 330 meters/second for the metric crowd divided by twice the room's longest dimension; 57Hz for a small 10' long room, 28Hz for a 20' room); with an infinitely rigid room producing 12dB/octave. The excess low-bass from a sub which is flat below the room's fundamental resonance can make a system sound slow. This could be fixed by a sub-woofer with a higher mechanical high-pass frequency (which wouldn't sell well, because consumers buy based on frequency extension) or an electronic filter.
Some placements are problematic.
Bass source and lister locations determine what room modes will affect you. Big room modes (you can have over 10dB, or 10X the acoustic power) at the wrong frequency (I've found the 70Hz height mode to be especially noticeable) can produce a one-note sound.
Parametric equalization can fix it for one location, but audiophiles often aren't into that sort of thing.