Playing drums and bass by one person.

Check out Kenwood Dennard's "Meta-Rhythmic Orchestra" ...not bass+drums per se, but keyboards+drums, including some basslines played on the keys. Basically a one man band.

Will it add some positive influence? I'm sure it positively influenced Kenwood's development as a musician, but obviously it didn't influence a whole lot of other musicians to follow suit.

 

Check out Knee body.
The drummer also plays the bass at the same time when he does his solo thing.
His name is Nate wood

 

There's an extremely popular band in my area called Sirsy, who are a guitar/drum duo. The bass duties are sometimes played by the guitarist, using foot pedals, and sometimes handled by the drummer, using this Roland synth gizmo she has on her drum set. While their music has plenty of merit on its own, I think the novelty of this approach only adds to their appeal. Music starts about 4:45 in the following video:

 

I believe the answer depends on a few things:

1. Accuracy of possible drum lines. (Do I have to do Tom fills with my foot?)
2. Accuracy of bass lines. (Can I use both hands to play bass?)
3. Will the drum parts suffer when playing simultaneous bass? (Can I play time with kick, snare and hat?)
4. Will the bass parts suffer when playing simultaneous drums? (Do I have to switch to playing bass with my nose?)

There probably is a market for such a device, albeit a small one, if it is accurate.

 

I also remember seeing ProjeKct Six in concert back in 2006 -- Robert Fripp on guitar, and Adrian Belew on V-drums -- and one of the more memorable pieces involved Belew playing a bass line using the V-drums' MIDI capability (plus an auxiliary Roland Octapad iirc) to trigger pitches on a synthesizer, while grooving with the rest of the drumkit.