Feasibility of coupling internal hub gear and derailleur Price considerations apart, would it make sense to install together an internal hub gear and a derailleur?

I was thinking of it as a viable way to avoid having the front gears.
Given that most contemporary internal gear hubs are designed to take up the entire width of a normal rear hub (135mm), there isn't space to add a rear derailleur cassette unless you have an abnormally wide rear frame. Perhaps you could try it with a fat tire bike but most regular bikes don't have the hub spacing to do this with regular IGHs.

And would it make sense? Not normally. Most contemporary internal-gear hubs have a wide-enough range (Shimano 7 speed has 245%; Shimano 8 speed has 307%; Rohloff 526%) and enough 'steps' to satisfy most of what you'd want with a derailleur. Bicyclists tend to be conservative and want to reduce the number of moving parts (and thus breakage points) to a minimum: having both IGH and a rear derailleur increases friction and doubles your maintenance and repair profile.

That being said, Brompton 6-speed bikes combine a 3-speed internal gear with a 2-speed rear mini-derailleur. This is in part to make up with the wide spacing of the 3-speed internal-gear hub. It wouldn't have been necessary if you had a 7- or 9-speed Shimano or 14-speed Rohloff, but the Brompton has a very narrow rear frame and only a custom 3-speed IGH fits. The Brompton IGH was initially made by Sturmey-Archer, then they switched to SRAM.



And as @armb has so cogently noted, SRAM does have a "Dual Drive" line that has a three-speed IGH combined with a rear derailleur.  It's unclear if any bike manufacturers in the USA have adopted the DD-3, although @gschenk noted in chat that:


  three speed hubs with seven speed cassettes are/were fairly common here in Germany. It's an old Sachs thing. Advantage: Without a front derailleur a chain guard may be mounted. While it still offers 3x7 gears.
  That dates back at least to the eighties (maybe but seven then). It is rare now, most bikes appear to be seven speed IGH. 





Finally, with all that being said, you could use a front derailleur with an IGH rear hub if you wanted extra mountain climbing gearing (there's also front internal-hub cranks). Some people put schlumpf mountain drives on their Bromptons so that they have a 3-speed IGH, a 2-speed rear derailleur, and 2-speed IG front crank.